Question

find the length of the third side. if necessary, round to the nearest tenth. \
8 \
11.7 \
64 \
136

Explanation:

Step1: Identify triangle type

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

Step2: Apply Pythagorean theorem

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

Step3: Calculate the square root

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

Answer:

8 (corresponding to the option "8")