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Chapter 0: Problem 39

A 20 -foot ladder is 15 feet from a house. How far up the house, to the nearest tenth of a foot, does the ladder reach?

Short Answer

Expert verified
The ladder reaches approximately 13.23 feet (to the nearest tenth of a foot, 13.2 feet) up the house.

Step by step solution

01

Identify Known Dimensions

Firstly, identify the known lengths or distances in the problem. Here, the length of the ladder, which is the hypotenuse of the right triangle, is 20 feet. The distance from the house, which is one of the two shorter sides or legs of the right triangle, is 15 feet.
02

Set Up the Pythagorean Theorem

Next, set up the Pythagorean theorem formula, which is a^2 + b^2 = c^2. Here, let's consider the 'a' as the distance of the ladder from the house (15 feet), the 'c' as the length of the ladder (20 feet). The 'b', which is the vertical distance of the ladder up the house, is what we need to find out.
03

Use the Pythagorean Theorem to Solve

Substitute the lengths we know from step 1 into the Pythagorean theorem. So, we have \(15^2 + b^2 = 20^2\). \nThis simplifies to 225 + b^2 = 400. \nTo solve for 'b', subtract 225 from each side of the equation to get: \(b^2 = 175\).\nTo find the value of 'b', square root both sides of the equation to get \(b \approx 13.23\).

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