Question

Use the pythagorean theorem to solve the problem. Round your answer to the nearest tenth if necessary.

A 12 foot ladder is placed 4 foot from the bottom of the house. How high will the ladder reach the house?

Answer 1

11.31 ft

Explanation:

Here in this problem ladder forms a right triangle with the wall of the house and it is acts as hypotenuse, length of one leg of right triangle given to be 4 feet.

Let the ladder reaches x ft height of the house.

Hence, by Pythagoras theorem:

`{12}^(2) = {4}^(2) + {x}^(2) \\ 144 = 16 + {x}^(2) \\ {x}^(2) = 144 - 16 \\ {x}^(2) = 128 \\ x = √(128) \\ x = 11.3137085 \\ x = 11.31 \: ft`

Hence, the ladder reaches 11.31 ft height of the house.