Question

Fill in the blanks!

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 \( b^2 \):
\[
b^2 = 289 - 64 \\
b^2 = 225
\]

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.