Question

question
find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Identify triangle type

It's a right triangle, so use Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c = 10\) (hypotenuse), \(a = 4\) (one leg), find \(b\) (other leg).

Step2: Apply Pythagorean theorem

Rearrange formula: \(b = \sqrt{c^2 - a^2}\)
Substitute values: \(b = \sqrt{10^2 - 4^2}\)
Calculate squares: \(b = \sqrt{100 - 16}\)
Subtract: \(b = \sqrt{84}\)
Simplify radical: \(b = \sqrt{4 \times 21} = 2\sqrt{21}\)

Answer:

\(2\sqrt{21}\)