After a severe storm, three sisters, April, May and June stood on their front porch and noticed that the tree in their front yard was leaning 3 degrees from vertical toward the house. From the porch, which is 101 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was 32 degrees. What is the height of the tree?.

Question

anonymous · Answer

We have:
AT cos 32 = AB
CT cos (90-3) = CT cos 87 = BC

Since all the angles in a triangle add up to 180 deg,
angle ATC = 180 - angle TAC - angle ACT
= 180 - 32- 87 = 61 deg

Now, by the sine rule,
sin ATC / AC = sin TAC / CT
which gives
CT = AC*sin TAC / sin ATC
or CT = 101*sin 32 / sin 61
or CT = 101*0.53/0.875 = 61.194 ft

The tree is 61.194 ft high