find all angles of a right triangle?

Question

Hypotenuse is 8 ft. One leg is 3 feet shorter than the next. Find remaining 2 sides to the nearest hundredth of an inch.

Answer 1

Pythagorean Theorem

a² + b² = c²

X² + (X - 3)² = 8²
2X² - 6X + 9 = 64

Subtract 64 from both sides and solve for x

2x² - 6x - 55 = 0

X = 6.95, X - 3 =3.95

sin x = (side opposite)/hypotenuse
sin x = 6.95/8 = 0.8692
angle x = 60.38 deg

Therefore
angle opposite X - 3 = 90 - 60.38 = 29.62 deg

and the angle opposite the hypotenuse is 90 deg
.

Answer 2

a^2 + b^2 = c^2, baby!!