Question

The hypotenuse of a right triangle is 6 inches. if one of the legs is 2 inches, find the degree measure of each angle

Answer 1

A and b are the 2 smaller sides, and c = hypotenus; only for right triangles,
Pythagorean Theorem states that:
${c}^{2} = {a}^{2} + {b}^{2}$
given c = 6 in., a = 2 in.
${c}^{2} = {a}^{2} + {b}^{2} \\ {6}^{2} = {2}^{2} + {b}^{2} \\ {b}^{2} = {6}^{2} - {2}^{2} = 36 - 4 \\ \sqrt{ {b}^{2} } = \sqrt{36 - 4} = \sqrt{32}$
$b = \sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2} \\ b = 5.66 \: inches$
So the three side are 2, 6, and 5.66 inches