Question

for the following right triangle, find the side length x. image of right triangle with vertical leg 8, horizontal leg 15, hypotenuse x

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Calculate the squares

\( 8^2 = 64 \) and \( 15^2 = 225 \). Then \( 64 + 225 = x^2 \).

Step3: Sum the values

\( 64 + 225 = 289 \), so \( x^2 = 289 \).

Step4: Take the square root

Taking the square root of both sides, \( x = \sqrt{289} = 17 \).

Answer:

17