Samuel needs to replace a portion of his rain gutter. The height of the roof is 25 feet and the length of his ladder is 30 feet. What is the maximum distance away from house that he can place
the ladder? Round your answer to the nearest foot.

Step-by-step explanation:

The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.

1. the hypotenuse is the length of the ladder which is 30 feet

2.the opposite is the height of the house, which is 25 feet

3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.

Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle

let the the opposite be x

we know that

Solving for x we have

Hence the maximum distance away from house that he can place

the ladder is 16.6 ft to the nearest foot