Question

find the length of the third side. if necessary, write in simplest radical form.
image of a right triangle with legs 4 and one leg 4√5, and the right angle between the leg of length 4 and the other leg (the third side we need to find)
answer
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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 \(c\) is hypotenuse, \(a,b\) legs. Here, \(c = 4\sqrt{5}\), one leg \(a = 4\), find the other leg \(b\).

Step2: Apply Pythagorean theorem

Rearrange formula: \(b^2 = c^2 - a^2\). Substitute values: \(c^2=(4\sqrt{5})^2 = 16\times5 = 80\), \(a^2 = 4^2 = 16\). So \(b^2 = 80 - 16 = 64\).

Step3: Solve for \(b\)

Take square root: \(b = \sqrt{64} = 8\).

Answer:

8