A 20-foot ladder leans against the side of a house with its base 3.5 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house.

Question

A 20-foot ladder leans against the side of a house with its base 3.5 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth.

Answer 1

NOTE: We must assume that the ground is level and is perpendicular to the wall of the house in order to solve this problem.

The wall and the ground form a right angle (90 degrees). The ladder which touches the ground and the wall forms the third side of a triangle. The side opposite the right angle (in this case the ladder) is called the hypotenuse. In right triangles, there is a formula to determine the length of the hypotenuse called the Pythagorean Theorem. It states that the sum of the squares of the 2 sides adjacent to the right angle are equal to the square of the hypotenuse. It is written as a² + b² = c² with c being the hypotenuse, or the ladder in this case.

We have been provided with the lengths of 2 sides of this triangle. The ladder which is the hypotenuse is 20 ft long and the bottom of the triangle is 3.5 ft. We can plug these into our formula a² + 3.5² = 20²

We can simplify this equation to a² + 12.25 = 400 which further simplified is a² = 387.75 which then gives us a = 19.69

This means that the distance from the ground up the wall to where the ladder is resting on the wall is 19.69 feet.