Question

A 12 feet ladder leans against the side of the house. The bottom of the ladder is 6 foot from the side of the house. How high is the top of the ladder from the ground? If necessary round your answer to the nearest 10th

Answer 1

The right angle triangle representing this scenario is shown below

From the triangle,

x represents the distance from the ground to the top of the ladder.

hypotenuse = longest side = 12

one leg = x

other leg = 6

We would find x by applying the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + oher leg^2

By substituting the values, we have

12^2 = x^2 + 6^2

144 = x^2 + 36

Subtracting 36 from both sides, we have

144 - 36 = x^2 + 36 - 36

108 = x^2

x^2 = 108

Taking the square root of both sides,

$x\text{ = }\sqrt[]{108}$

x = 10.4

The distance from the ground to the top of the ladder is 10.4 ft