John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the angle of elevation from where he is standing at 35 degrees. He walks 30 feet closer to the tree and finds that the angle of elevation has increased by 12 degrees. Estimate the height of the tree rounded to the nearest whole number.

Question

deathlynine · Answer

Let x be the distance from the tree. Now I did search this online so the following down bellow should help you. 
tan 47 = y/x 
tan 35 = y/(x + 30) 
x + 30 = y/tan 35 
x = y/tan 47 
Subtract: 
30 = (y/tan 35) - (y/tan 47) 
30 = y(1/tan35 - 1/tan 47) 
y = 30/(1/tan 35 - 1/tan47) 
y = 60.529 = 61 
tree = 61 + 6 = 67 feet

cublade · Answer

Thank you!