Question

question find the length of the third side. if necessary, write in simplest radical form. triangle with a right angle, one side labeled 10, another side labeled (10sqrt{2}) answer attempt 1 out of 2

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs. Here, we know two sides: one leg $a = 10$, the hypotenuse $c=10\sqrt{2}$, and we need to find the other leg $b$.

Step2: Apply the Pythagorean theorem

From $a^{2}+b^{2}=c^{2}$, we can re - arrange it to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Substitute $a = 10$ and $c = 10\sqrt{2}$ into the formula:

First, calculate $c^{2}=(10\sqrt{2})^{2}=10^{2}\times(\sqrt{2})^{2}=100\times2 = 200$

Then, calculate $a^{2}=10^{2}=100$

Now, $b=\sqrt{200 - 100}=\sqrt{100}=10$

Answer:

10