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. 12 cm
• B. 13 cm
• C. 15 cm
• D. 16 cm

Hint:

In a right triangle, use the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.

Answer 1

The Correct Option is C

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 \( \boxed{15} \).