Question

A 10 ft tall flagpole stands next to a tree. The shadow of the flagpole is 17 ft and the shadow of the tree is 50 ft. What is the height of the tree? Round to the nearest tenth if necessary.

Answer 1

If you imagine that the flagpole casts a shadow that is 17 feet, the sun should should cast a shadow at the same angle.

Therefore, we have a pair of similar triangles (by the AAA rule).

Now all you need to do is make a ratio of those side lengths

10/17 = 50/x

To solve for x, we do the following:

Multiply both sides by x to get

10x/17 = 50

Now multiply by 17 to get

10x = 850

Now, divide both sides by 10 to find the final answer

x = 85 feet

Explanation:

Answer 2

set up the proportion and then cross multiply to solve for the missing variable.

`(flagpole (height))/(flagpole (shadow)) = (tree (height))/(tree (shadow))`

⇒
`(10)/(17) = (x)/(50)`

⇒ 10(50) = 17(x)

⇒ 50 = 17x

⇒
`(50)/(17) = (17x)/(17)`

⇒ 2.9 = x

Answer: 2.9 ft