(i) A tower is 50 m high. Its shadow is x m shorter when the Sun's altitude is \[{{45}^{o}}\]than when it is \[{{30}^{o}},\] then x = ___. |
(ii)The angle of elevation of the top of a tower from a point 100 m from the tower is \[{{45}^{o}}\] then the height of the tower is __. |
A)
(i) (ii) \[\begin{array}{*{35}{l}} 38.6\,m~ \\ \end{array}\] 102m
B)
(i) (ii) \[36.6\,m\] 100m
C)
(i) (ii) \[36.1\text{ }m\] 98m
D)
(i) (ii) \[39.6\,m\] 101m
Correct Answer: B
Solution :
(i) In \[\Delta ABC,\frac{AB}{BC}=\tan {{45}^{o}}\Rightarrow \frac{50}{BC}=1\] \[\therefore \] \[BC=50m\] Similarly, in \[\Delta ABD,\,\,\frac{AB}{BD}=\tan {{30}^{o}}\] \[\Rightarrow \] \[\frac{50}{BC+CD}=\frac{1}{\sqrt{3}}\] \[\Rightarrow \] \[50+x=50\,\sqrt{3}\] \[\Rightarrow \] \[x=50\sqrt{3}-50\] \[\Rightarrow \] \[x=36.6m\] (ii) In \[\Delta ABC,\] \[\frac{AB}{BC}=\tan {{45}^{o}}\] \[\Rightarrow \] \[\frac{AB}{100}=1\Rightarrow AB=100m\] \[\therefore \] Height of tower is 100 m.You need to login to perform this action.
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