10th Class Mathematics Some Applications of Trigonometry Question Bank

done Some Applications of Trigonometry Total Questions - 43

• question_answer1)
  From a distance of 100 m from the foot of a building, the angle of elevation of its top is \[\text{3}0{}^\circ \]. What is the height of the building?
  A)
  \[57.7\,m\] done clear
  B)
  \[100\sqrt{3}\,m\] done clear
  C)
  \[5.77\,m\]         done clear
  D)
         \[\frac{100}{3}\,m\] done clear
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• question_answer2)
  The angles of elevation of the top from two points on either side of a tree are\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \]. What is the height of the tree if the two points are 52 m apart?
  A)
  39 m                      done clear
  B)
         22.5 m done clear
  C)
  65 m                      done clear
  D)
         225 m done clear
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• question_answer3)
  The angle of depression of a car from the top of a 20 m high tower is\[\text{6}0{}^\circ \]. At what distance from the foot of the tower is the car?
  A)
  16m                       done clear
  B)
         8m done clear
  C)
  22m                       done clear
  D)
         12m done clear
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• question_answer4)
  The height of a kite from the ground is 100 Vim. If the angle of elevation from a point on the ground is\[\text{45}{}^\circ \], what is the length of the string of the kite?
  A)
  \[100\sqrt{3}\,m\]                           done clear
  B)
  \[100\sqrt{2}\,m\] done clear
  C)
  \[100\sqrt{6}\,m\]                           done clear
  D)
  100 m done clear
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• question_answer5)
  A 24 m tall tree was cut to a height from the ground. The top of the tree touching the ground makes an angle\[\text{3}0{}^\circ \]with the ground. At what height from the ground was the tree cut?
  A)
  4 m                                         done clear
  B)
  8 m done clear
  C)
  10 m                                      done clear
  D)
  6 m done clear
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• question_answer6)
  A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is\[\text{3}0{}^\circ \]. He moves 40 m towards the bank and finds the angle of elevation to be\[\text{6}0{}^\circ \]. What is the width of the river?
  A)
  24 m                                      done clear
  B)
  20 m done clear
  C)
  26 m                      done clear
  D)
         15 m done clear
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• question_answer7)
  The angles of elevation of the sun changes from\[\text{45}{}^\circ \]to\[\text{3}0{}^\circ \].Then the shadow of a tower on the ground increases by 10 m. What is the height of the tower?
  A)
  13.65m                 done clear
  B)
         13.56m done clear
  C)
  15.63m                 done clear
  D)
         15.36m done clear
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• question_answer8)
  From an aero plane at an altitude of 900 m, two cars moving towards it in the same direction are found to be\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the distance between the cars?
  A)
  415m                     done clear
  B)
         315.4m done clear
  C)
  380.4 m                done clear
  D)
         305 m done clear
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• question_answer9)
  From a tower of 200 m, the angles of depression of two buildings in opposite sides of the tower are found to be\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the distance between the buildings?
  A)
  415m                     done clear
  B)
         315.4m done clear
  C)
  200 m                    done clear
  D)
         305 m done clear
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• question_answer10)
  The angles of elevation of the top of a building from the ground floor and first floor of another building are\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \] respectively. If the first floor is 40 m above the ground floor, what is the height of the building?
  A)
  54.64m                 done clear
  B)
         94.64m done clear
  C)
  40m                                       done clear
  D)
  109.3m done clear
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• question_answer11)
  From two opposite ends of a 100 m wide road, the angles of elevation of the top of a clock tower are found to be\[\text{3}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the height of the clock tower?
  A)
  36.6 m                   done clear
  B)
         36 m done clear
  C)
  37 m                      done clear
  D)
         35.4 m done clear
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• question_answer12)
  Two buildings are 140 m apart. The angle of elevation of the top of a building as seen from the top of the other is\[\text{3}0{}^\circ \]. If the second building is 60 m tall, how tall is the first building?
  A)
  83 m                      done clear
  B)
         80.83 done clear
  C)
  84m                                       done clear
  D)
  140.83 done clear
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• question_answer13)
  What is the angle of elevation of a light source when the length of the shadow of a flag post is equal to its height?
  A)
  \[\text{45}{}^\circ \]       done clear
  B)
         \[\text{3}0{}^\circ \]  done clear
  C)
  \[\text{6}0{}^\circ \]       done clear
  D)
         (d)\[\text{9}0{}^\circ \] done clear
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• question_answer14)
  A ladder 19 m long is placed leaning against a wall. If the angle of elevation of the ladder is\[\text{6}0{}^\circ \], how far is the ladder from the wall?
  A)
  11 m                                      done clear
  B)
  9.5 m done clear
  C)
  10.5 m                   done clear
  D)
         9 m done clear
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• question_answer15)
  A gas balloon is tied with a 215 m long rope with an inclination of\[\text{45}{}^\circ \]with the horizontal. How high is the balloon?
  A)
  166m                     done clear
  B)
         178m done clear
  C)
  152m                     done clear
  D)
         184m done clear
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• question_answer16)
  From a 50 m tall building, the angles of depression of the top and foot of a temple are found to be 30° and 60° respectively. What is the height of the temple?
  A)
  36m                       done clear
  B)
         25.3m done clear
  C)
  33.33m                 done clear
  D)
         30m done clear
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• question_answer17)
  The angle of elevation of a flag on a school building is\[~\text{45}{}^\circ \]. Moving 40 m towards the building, the angle of elevation is found to be\[\text{6}0{}^\circ \]. What is the height of the flag from the ground?
  A)
  40 m                      done clear
  B)
         94.64 m done clear
  C)
  60 m                      done clear
  D)
         54.64 m done clear
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• question_answer18)
  The angle of elevation of the top of a 'Br tower from the foot of a hillock is\[\text{6}0{}^\circ \]. The angle of elevation of the top of the hillock from the foot of the tower is\[\text{3}0{}^\circ \]. If the hillock is 50 m, what is the height of the tower?
  A)
  50m                       done clear
  B)
         140m done clear
  C)
  100m                     done clear
  D)
         150m done clear
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• question_answer19)
  From a 200 m tall tower, the angles of depression of the top and bottom of a pole are\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \]respectively. What are the respective values of height and distance of the pole from the tower?
  A)
  133.33m, 115.46m done clear
  B)
  115.46m, 133.33m done clear
  C)
  115.33 m, 66.33m done clear
  D)
  145.46m.33m done clear
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• question_answer20)
  The string of a kite is 200m long. It makes an angle of\[\text{3}0{}^\circ \]with the ground. What is the height of the kite above the ground?
  A)
  120m                                     done clear
  B)
  150m done clear
  C)
  100m                     done clear
  D)
         200m done clear
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• question_answer21)
  An eagle flying at an altitude of 1200 m flies vertically above another eagle at the same time, when the angles of elevation of the two birds are\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \] respectively. How high above the second eagle is the first eagle flying?
  A)
  507.20 m                              done clear
  B)
  500 m done clear
  C)
  570.81 m              done clear
  D)
         300 m done clear
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• question_answer22)
  A 15 m long ladder placed vertically along a wall broke in such a way that its top touches the ground making an angle of\[\text{6}0{}^\circ \]with it. At what height from the ground did the ladder break?
  A)
  7.34m                    done clear
  B)
         8m done clear
  C)
  9.46 m                   done clear
  D)
         6.96 m done clear
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• question_answer23)
  From a window A, 10 m above the ground, the angle of elevation of the top C of a tower is \[\text{x}{}^\circ \], where \[\tan x{}^\circ =\frac{5}{2}\], and the angle of depression of the foot D of the tower is \[\text{y}{}^\circ \], where tan \[\text{tan}\,\text{y}{}^\circ =\frac{1}{4}\]. What is the height CD of the tower to the nearest metre?
  A)
  135m                                     done clear
  B)
  75m done clear
  C)
  59m                       done clear
  D)
         110m done clear
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• question_answer24)
  PQ is a tower standing on a horizontal plane, Q being the foot of the tower. A and B are two points on the plane such that\[\angle \text{BQP}\] is\[\text{9}0{}^\circ \], AB = 4 m. If \[\cot (\angle PAQ)=\frac{3}{10}\]and\[\cot (\angle PBQ)=\frac{1}{2}\], find the height of the tower.
  A)
  10m                                       done clear
  B)
  15m done clear
  C)
  18m                       done clear
  D)
         20m done clear
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• question_answer25)
  The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angles of elevation of the tops of the poles from the middle point of the line segment joining their feet are complementary to each other. Find the heights of the poles.
  A)
  21.21 m, 42.42m done clear
  B)
  36.63 m, 67.76 m done clear
  C)
  42.24m.10.01 m done clear
  D)
  16.16m, 22.22m done clear
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• question_answer26)
  The shadow of a person X, when the angle of elevation of the sun is a, is equal in length to the shadow of person Y, when angle of elevation of the sun is\[\left( \frac{\alpha }{2} \right)\]. Which one of the following is correct?
  A)
  X is shorter than Y. done clear
  B)
  X is twice as tall as Y. done clear
  C)
  X is taller than Y but is not twice as tall as Y. done clear
  D)
  Both X and Y are of equal of height. done clear
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• question_answer27)
  Two observers are stationed north of a tower at a distance of 20 m from each other. If the elevation of the tower observed by them are \[\text{3}0{}^\circ \]and\[\text{45}{}^\circ \], respectively, find the height of the tower.
  A)
  10m                                       done clear
  B)
  16.32m done clear
  C)
  \[10(\sqrt{3}+1)m\]   done clear
  D)
         30m done clear
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• question_answer28)
  If the angle of depression and elevation of the top of a tower of height 'h' from the top and bottom of a second tower are x and y respectively, find the height of the second tower.
  A)
  \[h(\cot y-\cot x)\] done clear
  B)
  \[h(\tan x+\tan y)\] done clear
  C)
  \[h(1+\tan x\cot y)\] done clear
  D)
  \[h(\tan y.\cot x+1)\] done clear
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• question_answer29)
  Two posts are 25m and 15m high and the line joining their tops makes an angle of\[\text{45}{}^\circ \]with the horizontal. What is the distance between these posts?
  A)
  5 m                         done clear
  B)
         \[\frac{10}{\sqrt{2}}m\] done clear
  C)
  10m                       done clear
  D)
         \[10\sqrt{2}\,m\] done clear
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• question_answer30)
  The angle of elevation of the top of an incomplete tower at a point 40 m from its base is\[\text{45}{}^\circ \]. If the elevation of the completed tower at the same point is\[\text{6}0{}^\circ \], find the height through which the tower has been raised.
  A)
  \[40\sqrt{3}m\]                                done clear
  B)
  \[40(\sqrt{3}+1)m\] done clear
  C)
  \[40\left( 1-\frac{1}{\sqrt{3}} \right)m\] done clear
  D)
         \[40(\sqrt{3}-1)m\] done clear
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• question_answer31)
  The angle of elevation of an object from a point 500 m above a lake is observed to be \[\text{3}0{}^\circ \] and the angle of depression of its reflection in the lake is\[~\text{45}{}^\circ \]. Find the height of the object above the lake.
  A)
  \[\frac{500}{\sqrt{3}}(1+\sqrt{3})m\] done clear
  B)
         \[500(2+\sqrt{3})m\] done clear
  C)
  \[500(3+\sqrt{3})m\] done clear
  D)
         \[500(4+\sqrt{3})m\] done clear
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• question_answer32)
  A flag - staff is fixed at the top of a tower. The angles of elevation of the top and the bottom of this flag-staff at a point distant 'a' m from the foot of the tower, are\[\alpha \]and\[\beta \], respectively. Find the height of the flag -staff (in m).
  A)
  \[a(\sin \alpha -\sin \beta )\] done clear
  B)
         \[a(\cos \beta -\cos \alpha )\] done clear
  C)
  \[a(\tan \alpha -\tan \beta )\] done clear
  D)
         \[a\tan (\alpha -\beta )\] done clear
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• question_answer33)
  The height of a tower is h m and the angle of elevation of the top of the tower is a. On moving a distance h/2 towards the tower, the angle of elevation becomes P. What is the value of\[\cot \alpha -\cot \beta \]?
  A)
  \[\frac{1}{2}\]                    done clear
  B)
         \[\frac{2}{3}\] done clear
  C)
  1                              done clear
  D)
         2 done clear
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• question_answer34)
  From the top of a 60 m high tower, the angle of depression of the top and bottom of a building are observed to be\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \] respectively. Find the height of the building.
  A)
  \[60\sqrt{3}\,m\]             done clear
  B)
         \[40\sqrt{3}\,m\] done clear
  C)
  40 m                      done clear
  D)
         20 m done clear
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• question_answer35)
  A landmark on the bank of a river is observed from two points X and Y on the opposite banks of the river. The lines of sight make equal angles with the bank of the river. If XY = 1 km, what is the width of the river?
  A)
  \[\frac{3}{2}km\]             done clear
  B)
         \[\frac{1}{2}km\] done clear
  C)
  \[\frac{3\sqrt{2}}{2}km\]              done clear
  D)
         \[\frac{3\sqrt{3}}{2}km\] done clear
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• question_answer36)
  A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is\[\text{45}{}^\circ \]. Which of the following is true?
  A)
  Breadth of the river is twice the height of the tower. done clear
  B)
  Height of the river is twice the breadth of the river. done clear
  C)
  The height of the tower and the breadth of the river are equal. done clear
  D)
  Breadth of river is thrice the height of the tower. done clear
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• question_answer37)
  The angles of elevation of the top of a vertical tower from points at distance a and b from the base and in the same line with it are complementary. If a > b, find the height of the tower.
  A)
  \[\sqrt{ab}\]      done clear
  B)
         \[\sqrt{(a+b)}\] done clear
  C)
  \[\sqrt{(a/b)}\] done clear
  D)
         \[\sqrt{(b-a)}\] done clear
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• question_answer38)
  A tower subtends an angle of\[~\text{3}0{}^\circ \]at a point on the same level as the foot of the tower. At a second point h m above the first, the depression of the foot of the tower is 60°. What is the horizontal distance of the tower from the point?
  A)
  \[\text{h cot 6}0{}^\circ \]            done clear
  B)
         \[\text{h cot 3}0{}^\circ \] done clear
  C)
  \[\frac{h}{2}\text{cot 6}0{}^\circ \]          done clear
  D)
         \[\frac{h}{2}\text{cot 3}0{}^\circ \] done clear
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• question_answer39)
  Starting from the same point in a leveled field, Rahul walked 1000 m due East and then 1000 m due North whereas Aryan walked 2000 m North-East. At the end of the walks, what is the distance between Rahul and Aryan?
  A)
  Zero                       done clear
  B)
         828 m done clear
  C)
  586m                     done clear
  D)
         1000m done clear
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• question_answer40)
  If a flag staff of 6 m height placed on the top of a tower throws a shadow of \[2\sqrt{3}m\]along the ground, find the angle that the sun makes with the ground.
  A)
  \[\text{6}0{}^\circ \]                       done clear
  B)
         \[\text{3}0{}^\circ \] done clear
  C)
  \[\text{45}{}^\circ \]                       done clear
  D)
         \[~\text{9}0{}^\circ \] done clear
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• question_answer41)
  The angle of elevation of a jetfighter from a point P on the ground is\[\text{6}0{}^\circ \]. After five seconds of flight, the angle of elevation changes to\[\text{45}{}^\circ \]. If the jet is flying at a height of 3000 m. find the speed of the jet, in m/s.
  A)
  \[1000(3-\sqrt{3})\] done clear
  B)
         \[200(3-\sqrt{3})\] done clear
  C)
  \[1000\sqrt{3}\]                done clear
  D)
         \[600\] done clear
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• question_answer42)
  The angles of elevation of the tops of two pillars of height h and 2h from a point on the line joining the feet of the two pillars are complementary. lf the distances of the feet of the pillars from that point are x and y respectively, find the value of 2h2.
  A)
  \[{{x}^{2}}y\]                     done clear
  B)
         \[x{{y}^{2}}\] done clear
  C)
  \[xy\]                    done clear
  D)
         \[{{x}^{2}}{{y}^{2}}\] done clear
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• question_answer43)
  A round balloon of radius 'r' subtends an angle\[\alpha \]at the eye of an observer, while the angle of elevation of its centre is\[\beta \]. Find the height of the centre of the balloon.
  A)
  \[r\sin \frac{\alpha }{2}\cos ec\beta \] done clear
  B)
         \[r\cos ec\frac{\alpha }{2}\cos \beta \] done clear
  C)
  \[r\cos \frac{\alpha }{2}\cos ec\beta \] done clear
  D)
         \[r\cos ec\frac{\alpha }{2}\sin \beta \] done clear
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