Railways
Sample Paper
RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-19
question_answer
The height of a tower is 100 m. From its top and middle point, the top of a hill is observed to have angles of depression \[30{}^\circ \]and\[60{}^\circ \] respectively. The height of the hill is
A) 158 m
B) 125 m
C) 120 m
D) 160 m
Correct Answer:
B
Solution :
Height of hill = x m and distance between tower and hill = y m Then, \[\tan 60{}^\circ =\frac{x-50}{y}\] \[\Rightarrow \] \[\sqrt{3}=\frac{x-50}{y}\] \[\Rightarrow \] \[x-\sqrt{3}y=50\] ?(i) and \[\tan 30{}^\circ =\frac{x-100}{y}\] \[\Rightarrow \] \[\frac{1}{\sqrt{3}}=\frac{x-100}{y}\] \[\Rightarrow \] \[\sqrt{3}-y=100\sqrt{3}\] ?(ii) After solving Eqs. (i) and (ii), x = 125 m