Question

Use the information in the diagram to determine the height of the tree to the nearest foot.

Answer 1

You are going to have to assume that the angle between the building and ground is a right angle (90 degrees) to solve this problem.

Now you can use right angle trigonometry or proportions

First find the measure of the angle formed by the hypotenuse (100 ft +120 ft) and the building height (176 ft). Call it angle A.

So we have: Tan(A)= 176/220 Using a calculator, angle A = 38.66 degrees

Using this angle, we can now solve for the height of the tree.

So we have: Tan(38.66) = height/100 ft

Rearranging, we get: 100 Tan(38.66) = 80 feet

Using proportions, we have this:

176/220 = height/100

Cross multiply and then divide. We get [(100)(176)}\]/220 = 80 ft.