question_answer

From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be \[30{}^\circ \]and \[60{}^\circ \]respectively. The height of the y tower is

A) 60 m

B) 75 m

C) 30 m

D) 45 m

Correct Answer: A

Solution :

[a] Let the height of the tower is h m From figure, In\[\Delta BMQ,\]\[\tan 30{}^\circ =\frac{90-h}{x}\] \[\Rightarrow \]   \[\frac{1}{\sqrt{3}=\frac{90-h}{x}}\]                  (i) In \[\Delta APQ,\]\[\tan 60{}^\circ =\frac{90}{x}\] \[\Rightarrow \]   \[x=\frac{90}{\sqrt{3}}=30\sqrt{3}\] On putting the value of x in Eq. (i), We get   \[\frac{1}{\sqrt{3}}=\frac{90-h}{30\sqrt{3}}\] \[\Rightarrow \]   \[90-h=30\] \[\Rightarrow \]   \[h=90-30=60\,m\]