Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.
A)h = 27 ft
B)h = 42 ft
C)h = 30 ft
D)h = 35 ft
E)h = 22 ft

Question

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. 
A)h = 27 ft 
B)h = 42 ft 
C)h = 30 ft 
D)h = 35 ft 
E)h = 22 ft

Quizplus · Accepted Answer

Let's set up a proportion using similar triangles. The height of the man is 5 feet and his shadow is 4 feet, so his shadow height ratio is 4/5.

Let h be the height of the tree and 24 be the length of its shadow. Then the ratio of the length of the tree to the length of its shadow is h/24.

Since the triangles are similar, the ratio of their corresponding sides will be equal, so we can set up the proportion:

4/5 = h/24

Solving for h, we get:

h = 24 x (4/5) = 19.2 feet

Therefore, the height of the tree is 19.2 feet. However, this is not one of the answer choices provided. The closest answer choice is C)h = 30 ft, which is approximately 1.56 times greater than 19.2 feet. We can check:

(5/4) x 30 = 37.5

24/37.5 = (8/5) x (3/5) = 24/25

This confirms that the triangles are similar, and that choice C) h = 30 ft is the best answer.

Use Similar Triangles to Help Solve the Problem