Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

$$a^2 + b^2 = c^2$$
Here, $a=10$, $c=13$, $b=x$, so:
$$10^2 + x^2 = 13^2$$

Step2: Calculate squared values

$$100 + x^2 = 169$$

Step3: Isolate $x^2$

$$x^2 = 169 - 100 = 69$$

Step4: Solve for $x$ and round

$$x = \sqrt{69} \approx 8.31$$

Answer:

8.31