Questions: For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Solution Steps

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is 16, and the other two sides are 8 and x. So, we have:

$x^2 + 8^2 = 16^2$

$x^2 + 64 = 256$

Subtract 64 from both sides:

$x^2 = 192$

Take the square root of both sides:

$x = \sqrt{192}$

$x \approx 13.8564$ Rounding to the nearest hundredth gives: $x \approx 13.86$

Final Answer: The final answer is $\boxed{13.86}$