Question

find the length of the third side. if necessary, write in simplest radical form.
triangle with legs 6, 10, right angle
answer attempt 2 out of 2
input box with 8
submit answer

Explanation:

Step1: Identify triangle type

It's a right - triangle, so use Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\), where \(c\) is hypotenuse, \(a,b\) are legs. Here, hypotenuse \(c = 10\), one leg \(b = 6\), find the other leg \(a\).

Step2: Apply Pythagorean theorem

Rearrange formula to \(a=\sqrt{c^{2}-b^{2}}\). Substitute \(c = 10\), \(b = 6\): \(a=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}\).

Step3: Simplify the radical

\(\sqrt{64}=8\).

Answer:

8