Question

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

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Let \(a = 6\), \(c=10\), and we need to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values

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

$$
LATEXBLOCK0
$$

Step3: Solve for \(b\)

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

Answer:

\(8\)