Question

b) A surveyor measures the angle of elevation of the top of a perpendicular building as 19°. He moves 120 m nearer the building and finds the angle of elevation is now 47°. Determine the height of the building.

Answer 1

Step-by-step explanation:

Let x be the original distance to the building and let h be the height of the building. Initially we have an angle of 19 degrees: tan(19)= h/x. Moving 120 m closer, so that the distance to the building is x- 120, we have an angle of 47 degrees: tan(47)= h/(x- 120).

Tan(19)= 0.3443 and tan(47)= 1.0723 so we have h/x= 0.3443 which gives h= 0.3443x. That makes the second equation 1.0723= 0.3443x/(x- 120).

Can you solve for x and then h?