Question

In (triangle symbol)ABC, (angle symbol)C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.

a =3, c =19

Answer 1

Use the Pythagorean Theorem.

a² + b² = c²

3² + b² = 19²

9 + b² = 361

b² = 352

b = 4√11

Now, solve for the remaining angles by using the trigonometric ratios:

Sine = opposite/hypotenuse

sin(A)= 3/19

sininverse(3/19) = 9.1 = angle A

180-9.1-90 = 80.9 = angle B