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 \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse. Here, \( a = 10 \), \( b = 7 \), and \( x \) is the hypotenuse. So we have \( 10^2 + 7^2 = x^2 \).

Step2: Calculate the squares

\( 10^2 = 100 \) and \( 7^2 = 49 \). Then \( 100 + 49 = x^2 \), which simplifies to \( 149 = x^2 \).

Step3: Solve for x

Take the square root of both sides: \( x = \sqrt{149} \). Calculate \( \sqrt{149} \approx 12.21 \) (rounded to the nearest hundredth).

Answer:

\( 12.21 \)