Jack wants to build a tree house.

Question

His parents worry that he is building it too high. If Jack’s dad is looking at the tree house location from a 39° angle and then moves back 10 feet so he can see it at a 31° anglehow high is the tree house location?

Answer 1

Drawing a figure with the h=height of playhouse and x being the distance of where the 39° is measured, and x+10 where the 31° is measured from:

Tan 39 = h/x

Tan 31 = h/(x+10)

Solving shows x is 23.3 feet away yielding h = 23.3 feet.