Fill in the blanks!

Question

An unknown leg of a right traingle can be found using the Pythagorean theorem.

Pythagorean theorem: a^(2) + b^(2) = c^(2)
Traingle: 8ft, 17ft, b

a^(2) + b^(2) = c^(2)
_^(2) + b^(2) = _
b^(2) = 289 - 64
b^(2) = _
\sqrt(b^(2) = \sqrt(225)
b = _ft

Answer 1

Let's fill in the blanks step by step.

1. You have a right triangle with sides: one leg $a=8\text{ ft}$, the other leg $b$, and the hypotenuse $c=17\text{ ft}$.

Using the Pythagorean theorem formula $a^2+b^2=c^2$:

1. Substitute the known values: $$8^2+b^2={17}^2$$

2. Fill in the equation: $$8^2+b^2={17}^{2}64+b^2=289$$

3. To find $b^2$: $$b^2=289-64b^2=225$$

4. Now, take the square root of both sides: $$b=\sqrt{225}$$

5. Solve for $b$: $$b=15\text{ ft}$$

Now, here's the completed version with the blanks filled in:

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An unknown leg of a right triangle can be found using the Pythagorean theorem.

Pythagorean theorem: $a^2+b^2=c^2$
Triangle: 8 ft, 17 ft, b

$a^2+b^2=c^2$
$8^2+b^2={17}^2$
$64+b^2=289$
$b^2=289-64$
$b^2=225$
$\sqrt{b^2}=\sqrt{225}$
$b=15$ ft

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Thus, the unknown leg $b$ is 15 ft.