Question

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

Answer 1

The answer is 80 ft. 

Based on the diagram we know that the tree triangle and the building triangle are similar triangles where the lengths of each are proportional to the other. 

The lengths of the triangle the tree makes are half of the lengths of the building triangle. So this problem can be solved using ratio and proportion:

$\frac{144}{160} = \frac{72}{x}$

to solve for x, all you need to do is cross multiply then divide. 

$\frac{160*72}{144} =x$

The answer is then 80ft.

Another way to solve this is just by using logic. If the lengths of the tree triangle is half of the building, simply divide the lengths of the building triangle by two. 

160ft/2 = 80ft.