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 42 Page 500

The value of x is 12sqrt(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. 12^2+ 12^2= x^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.
12^2+12^2=x^2
â–Ľ
Solve for x
144+144=x^2
288=x^2
x^2=288
x=sqrt(288)
x=sqrt(2*144)
x=sqrt(2)*sqrt(144)
x=sqrt(2)* 12
x=12sqrt(2)
The value of x is 12sqrt(2).

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