Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth. right triangle image with legs 6 and x, hypotenuse 10

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, \( c = 10 \), one leg \( a = 6 \), another leg \( b = x \). So \( 6^2 + x^2 = 10^2 \).

Step2: Solve for \( x^2 \)

Calculate \( 6^2 = 36 \), \( 10^2 = 100 \). Then \( x^2 = 100 - 36 = 64 \)? Wait, no, wait: Wait, 100 - 36 is 64? Wait, no, 10 squared is 100, 6 squared is 36, so \( x^2 = 100 - 36 = 64 \)? Wait, no, that would make x=8, but wait, maybe I mixed up. Wait, no, the hypotenuse is 10, one leg is 6, so the other leg: \( x^2 + 6^2 = 10^2 \), so \( x^2 = 100 - 36 = 64 \), so \( x = \sqrt{64} = 8 \)? Wait, but 6-8-10 is a Pythagorean triple. Wait, maybe the problem is correct. Wait, let me check again. \( 6^2 = 36 \), \( 10^2 = 100 \), so \( x^2 = 100 - 36 = 64 \), so \( x = 8.00 \) when rounded to nearest hundredth.

Answer:

8.00