Question

1. find the missing side of the right triangle. side c is the hypotenuse. sides a and b are the legs. leave your answers in simplest radical form.

b = √6 yd, c = 4 yd.

a =

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\). We need to solve for \(a\), so rearrange the formula to \(a^2 = c^2 - b^2\).

Step2: Substitute given values

Given \(b = \sqrt{6}\) yd and \(c = 4\) yd. Substitute into the formula: \(a^2 = 4^2 - (\sqrt{6})^2\).

Step3: Simplify the equation

Calculate \(4^2 = 16\) and \((\sqrt{6})^2 = 6\). So \(a^2 = 16 - 6 = 10\).

Step4: Solve for \(a\)

Take the square root of both sides: \(a = \sqrt{10}\) (since length can't be negative, we take the positive root).

Answer:

\(\sqrt{10}\) yd