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Home > CCAA > Chapter 10 Unit 11 > Lesson CC3: 10.1.2 > Problem 10-28

10-28.

Find the length of the side labeled $x$ in each of the right triangles pictured below. Identify each answer as a rational or irrational number.

Hint:

Use the Pythagorean Theorem.

Hint (a):
$(\text{leg } 1)^2 + (\text{leg } 2)^2 = (\text{hypotenuse})^2$
Substitute the values that are given.
Step 1 (a):
$(5)^2 + (x)^2 = (13)^2$
$25 + x^2 = 169$
Step 2 (a):
Solve by isolating $x$ .
Step 3 (a):
$x^2 = 144$
Take the square root of each side to get the answer.

Hint (b):
$(\text{leg } 1)^2 + (\text{leg } 2)^2 = (\text{hypotenuse})^2$
Substitute the values that are given.
More Help (b):
$(6)^2 + (3)^2 = (x)^2$
Now solve for $x$ .

Hint (c):
See part (a).
Answer (c):
$8$

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