Question

find the length of the third side. if necessary, write in simplest radical form. triangle image with leg 4, hypotenuse 10, right angle at bottom left

Explanation:

Step1: Identify triangle type

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

Step2: Apply Pythagorean theorem

Rearrange formula: \(a^2 = c^2 - b^2\). Substitute \(c = 10\), \(b = 4\): \(a^2 = 10^2 - 4^2 = 100 - 16 = 84\).

Step3: Simplify radical

\(a = \sqrt{84} = \sqrt{4 \times 21} = 2\sqrt{21}\).

Answer:

\(2\sqrt{21}\)