Question

A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach? 2.4 feet 6.0 feet 9.2 feet 10.8 feet

Answer 1

9.2 feet

Explanation:

The ladder forms a right angle triangle with the ground and the tree

10² = 4² + h²

h² = 100 - 16

h² = 84

h = 9.16515139

Answer 2

C

Explanation:

If we were to draw a horizontal line from the bottom of the ladder to the bottom of the tree and then draw a vertical line from the bottom of the tree to the top of the ladder, we'd get a right triangle with legs as the distance between the bottom of the tree and the bottom of the ladder and the height of the ladder, and the hypotenuse is the length.

Here, we know the hypotenuse is 10 feet and that the bottom of the ladder is 4 feet away from the bottom of the tree, so use the Pythagorean Theorem to find the height:

h =
`√(10^2-4^2) =√(84)` ≈ 9.2 feet

The answer is C.