Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
5. The Sine and Cosine Ratios
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Exercise 44 Page 500

The value of x is 6sqrt(2) and the side lengths do not form a Pythagorean Triple.

Practice makes perfect

Let's begin with recalling the Pythagorean Theorem.

In the formula, a and b are the legs while c is the hypotenuse of a right triangle. Now let's take a look at the given triangle.
To find x, we will write the equation according to the Pythagorean Theorem. 3^2+ x^2= 9^2 Let's solve above equation. Since x is a side length, we will consider only positive case when taking a square root of x^2.
3^2+x^2=9^2
â–Ľ
Solve for x
9+x^2=81
x^2=72
x=sqrt(72)
x=sqrt(36*2)
x=sqrt(36)*sqrt(2)
x=6sqrt(2)
The value of x is 6sqrt(2).

Notice that not all side lengths of the triangle are integers, so they do not form a Pythagorean triple.