Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth. x 13 7

Explanation:

Step1: Apply Pythagorean theorem

In 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 \( c = 13 \), one leg \( b = 7 \), and the other leg \( a = x \). So we have \( x^2 + 7^2 = 13^2 \).

Step2: Solve for \( x^2 \)

Calculate \( 7^2 = 49 \) and \( 13^2 = 169 \). Then \( x^2 = 169 - 49 = 120 \).

Step3: Solve for \( x \)

Take the square root of both sides: \( x = \sqrt{120} \approx 10.95 \) (rounded to the nearest hundredth).

Answer:

\( 10.95 \)