McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
2. The Pythagorean Theorem and Its Converse
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Exercise 19 Page 634

Evaluate the length of the horizontal portion using the Pythagorean Theorem.

≈ 3 ft.

Practice makes perfect

Let's begin with recalling the Pythagorean Theorem. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

a^2+ b^2= c^2 Now, let's look at the given picture which presents the support for a basketball hoop. As we can see, the support forms a right triangle.

Therefore, we can use the Pythagorean Theorem to evaluate the value of x. Notice that, since x represents the side length, we will consider only the positive case when taking a square root of x^2.
( 1 12)^2+ x^2=( 3 13)^2
Solve for x
(3/2)^2+x^2=(10/3)^2
3^2/2^2+x^2=10^2/3^2
9/4+x^2=100/9
x^2=100/9-9/4
x^2=400/36-9/4
x^2=400/36-81/36
x^2=319/36
sqrt(x^2)=sqrt(319/36)
x=sqrt(319/36)
x=sqrt(8.8611...)
x=2.9767...
x≈ 3
The length of the horizontal portion of the support is approximately 3 feet.