Question:
A right triangle has one leg of 8 cm and a hypotenuse of 17 cm. What is the length of the other leg?
Options
A right triangle has one leg of 8 cm and a hypotenuse of 17 cm. What is the length of the other leg?
Options
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In a right triangle, use the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.
Updated On: Oct 4, 2025
- 12 cm
- 13 cm
- 15 cm
- 16 cm
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The Correct Option is C
Solution and Explanation
Recall the Pythagorean theorem, which relates the three sides of a right triangle:
\[
a^2 + b^2 = c^2
\]
Where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. In this problem, we are given:
\[
a = 8,
c = 17,
\text{and we need to find}
b. \] Substitute the known values into the Pythagorean theorem: \[ 8^2 + b^2 = 17^2 \] \[ 64 + b^2 = 289 \] Now, subtract 64 from both sides: \[ b^2 = 289 - 64 = 225 \] Take the square root of both sides to solve for \( b \): \[ b = \sqrt{225} = 15 \] Thus, the length of the other leg is \( \boxed{15} \).
c = 17,
\text{and we need to find}
b. \] Substitute the known values into the Pythagorean theorem: \[ 8^2 + b^2 = 17^2 \] \[ 64 + b^2 = 289 \] Now, subtract 64 from both sides: \[ b^2 = 289 - 64 = 225 \] Take the square root of both sides to solve for \( b \): \[ b = \sqrt{225} = 15 \] Thus, the length of the other leg is \( \boxed{15} \).
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