To determine the height of a tree, you measure its shadow and the shadow of a five-foot lamppost. The shadow of the lamppost is 4 feet and the shadow of the tree is 45 feet. Assuming both the tree and the lamppost are standing next to each other and perpendicular to the ground, how tall is the tree? Round to the nearest tenth of a foot.
A)56.3 feet
B)42.8 feet
C)49.5 feet
D)36.0 feet
E)59.6 feet

Question

Quizplus · Accepted Answer

Using similar triangles, the ratio of the height of the tree to its shadow is the same as the ratio of the height of the lamppost to its shadow. So, $ \frac{height\ of\ tree}{45\ feet} = \frac{5\ feet}{4\ feet} $. Solving for the height of the tree gives $ height\ of\ tree = \frac{5\ feet}{4\ feet} \times 45\ feet = 56.25\ feet $, which rounds to 56.3 feet.

To Determine the Height of a Tree, You Measure Its