Please can someone show me the steps to do this problem?? Also, please don't tell me to just google the solution because I've already tried and have tried to do this problem by myself for hours now...Thank you so much.

Question

You are measuring trees in a forest. Standing on the ground exactly half -waybetweentwo trees, you measure the angle the top of each tree makes with the horizon: one angle is 67◦, and the other is 82◦. If one tree is 80 feet taller than the other, how far apart (horizontal distance along the ground) are the two trees?

Answer 1

make a diagram, showing the two trees at A and B, labeled h for the height of the shorter, and h+80 for the height of the taller.
let P be the midpoint of AB , where AP = BP
Then the angle at P for the taller tree is 82° , and the angle at P for the smaller tree is 67°

then h/AP = tan67° and (h+80)/BP = tan82°
AP = h/tan67 and BP = (h+80)/tan82
but AP and BP are equal, so

h/tan67 = (h+80)/tan82
htan82 = htan67 + 80tan67
htan82 - htan67 = 80tan67
h(tan82-tan67) = 80tan67
h = 80tan67/(tan82-tan67) = .....

You do the button - pushing

once you have h, sub it back into the little equation for AP

(I got AP= 16.8)

Answer 2

What does tan67 equal?