Question

An engineer determines that the angle of elevation from her position to the top of a tower is 52°. She measures the angle of elevation again from a point 47 meters farther away from the tower and

finds it to be 31°. Both positions are due east of the town. Find the height of the tower

pls help

Answer 1

Explanation:

The question is illustrated with the attached image.

Angle of elevation is the angle between a line of sight and the horizontal surface.

Let h be the height of the tower

First, calculate distance BC (x).

This is calculated using the following tan ratio,

tan52=h/x

h=xtan52

From the attached image:,

CD=47+x

tan31=h/x+47

h=(x+47)tan31

xtan52=(x+47)tan31,

solving for x we get, x=41.156m

h=xtan52=41.156 * tan52=53.2m