Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be \( a \). According to the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c = 10 \) (hypotenuse) and \( b = 6 \). So \( a^{2}=c^{2}-b^{2} \).

Step2: Substitute values

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

Step3: Solve for \( a \)

Take the square root of both sides: \( a=\sqrt{64}=8 \).

Answer:

\( 8 \)