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, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, hypotenuse \( c = 13 \), one leg \( a = 10 \), another leg \( x \). So \( 10^2 + x^2 = 13^2 \).

Step2: Solve for \( x^2 \)

\( x^2 = 13^2 - 10^2 = 169 - 100 = 69 \).

Step3: Find \( x \)

\( x = \sqrt{69} \approx 8.31 \).

Answer:

\( 8.31 \)