The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower an

Question

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

Accepted Answer

Let the height of the tower be $h$. The distances are $a = 4$ m and $b = 9$ m. Since the angles are complementary, if one is $	heta$, the other is $90^\circ - 	heta$. We have $	an 	heta = \frac{h}{4}$ and $	an(90^\circ - 	heta) = \frac{h}{9} \implies \cot 	heta = \frac{h}{9}$. Multiplying both equations: $	an 	heta \cdot \cot 	heta = \frac{h}{4} \cdot \frac{h}{9} \implies 1 = \frac{h^2}{36} \implies h^2 = 36 \implies h = 6$ m.

Applications of Trigonometry

❓ Sibling Questions in this Chapter