Question

for the following right triangle, find the side length x.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a, b \) are the legs. Here, hypotenuse \( c = 15 \), one leg \( a = 8 \), and the other leg is \( x \). So we have \( 8^2 + x^2 = 15^2 \).

Step2: Solve for \( x^2 \)

Calculate \( 8^2 = 64 \) and \( 15^2 = 225 \). Then \( x^2 = 225 - 64 = 161 \).

Step3: Solve for \( x \)

Take the square root of both sides: \( x = \sqrt{161} \approx 12.69 \) (or leave it as \( \sqrt{161} \)).

Answer:

\( \sqrt{161} \) (or approximately \( 12.69 \))