Let's fill in the blanks step by step.
- 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 \( a^2 + b^2 = c^2 \):
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Substitute the known values: \[ 8^2 + b^2 = 17^2 \]
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Fill in the equation: \[ 8^2 + b^2 = 17^2 \ 64 + b^2 = 289 \]
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To find \( b^2 \): \[ b^2 = 289 - 64 \ b^2 = 225 \]
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Now, take the square root of both sides: \[ b = \sqrt{225} \]
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Solve for \( b \): \[ b = 15 \text{ ft} \]
Now, here's the completed version with the blanks filled in:
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
Thus, the unknown leg \( b \) is 15 ft.