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, \( c = 17 \), \( a = 12 \), \( b = x \). So \( 12^2 + x^2 = 17^2 \).

Step2: Solve for \( x^2 \)

Calculate \( 12^2 = 144 \), \( 17^2 = 289 \). Then \( x^2 = 289 - 144 = 145 \).

Step3: Find \( x \)

Take square root: \( x = \sqrt{145} \approx 12.04 \) (rounded to nearest hundredth).

Answer:

\( 12.04 \)