Trigonometry-13

From Homeworkwiki

The height of a tower is half the height of the flag staff at its top. The angle of elevation

of the top of the tower as seen from a distance of 10 m from its foot is 30⁰. Find the elevation

of the top of the flag staff from the same point.

solution: BC is the height of the tower; CD is the height of the flag staff.

Let BC = a m; then CD = 2a m; AB = 10 m.

∠BAC = 30⁰

Let angle BAD = A

BC / AB = tan 30⁰

BC = AB X tan 30⁰

= 10 X 1 / √3

Therefore, a = 10 / √3 m

= 3 X 10 / √3 = 10 √3 m

tan A = BD / AB = 10 √3 / 10 = √3

Hence, A = 60⁰

The elevation of the top of the flag staff from the same point A is 60⁰.