Please submit your concern

Question:

A tall tower has its base at point K. Three points A, B and C are located at distances of 4 metres, 8 metres and 16 metres respectively from K. The angles of elevation of the top of the tower from A and C are complementary. What is the angle of elevation (in degrees) of the tower’s top from B?

Explanation:

Given the distances are :
AE = 4 meters , EB = 8 meters and EC = 16 meters.
Considering the length of ED = K.
Given the angles DAE and angle DCE are complementary.
Hence the angles are A and 90 - A.
Tan(90 - A) = Cot A

tan DAE = $\frac{k}{4}$ and tan DCE = tan $\frac{1}{D A E}$ = $\frac{k}{16}$

Hence $\frac{k}{16}$ = $\frac{4}{k}$

k = 8 meters.
The angle DBE is given by

tan DBE = $\frac{k}{8}$ = 1

Hence the angle is equal to 45 degrees.

Please submit your concern

Feedback