A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.

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Question:

A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building. In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot

Answer:

The first step in solving a problem is illustrating it just as what the picture shows. The ladder represents the hypotenuse, or the longest side of the right triangle. It measures 14 feet. The base measures 6 feet. The height of the top of the ladder from the base of the wall is denoted as x. Since this is a right triangle, the special equations for Pythagorean theorems would apply. The equation is

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the other shorter legs. Substituting the values,

14^2 = 6^2 + x^2
x^2 = 14^2 – 6^2
x^2 = 160
x = 4√10 = 12.65 feet

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