a 60 meter high building is erected vertically on a hillside. An electric post stands vertically on the hill. An observer at the top the building, find the angle of depressions of the top and the bottom of the electric post to be 30 degrees and 42 degrees respectively. if the hill makes an angle of 20 degrees with the horizontal, how high is the electric post.

Answer 1

is the building uphill or downhill from the post?

If the building is downhill from the post, at a horizontal distance of x, then let

a = vertical distance from the base of the building to the base of the post
x = horizontal distance between building and post
h = height of post

a/x = tan20°
(60-a)/x = tan42°
(60-a-h)/x = tan30°

Nope, that gives a negative post height. So, how about the building is uphill from the post? Then we have

a/x = tan20°
(60+a)/x = tan42°
(60+a-h)/x = tan30°

Answer 2

thanks dude, i get the answer..