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