Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( x^{2}=a^{2}+b^{2} \), where \( a = 11 \) and \( b = 8 \). So we have \( x^{2}=11^{2}+8^{2} \).

Step2: Calculate the squares

Calculate \( 11^{2}=121 \) and \( 8^{2}=64 \). Then \( x^{2}=121 + 64=185 \).

Step3: Solve for x

Take the square root of both sides: \( x=\sqrt{185} \approx 13.60 \) (rounded to the nearest hundredth).

Answer:

\( 13.60 \)