Question

Find the cosine of ∠R.

image of a right triangle that has the following values, Angle Q, Angle P, Angle R, Line QP which has a length of 30, Line QR which has a length of 16, and Line PR which has an unknown length

Answer 1

If the right angle is at Q (so QP and QR are the legs), then PR is the hypotenuse. By the Pythagorean theorem

PR = sqrt(QP^2 + QR^2) = sqrt(30^2 + 16^2) = sqrt(900 + 256) = sqrt(1156) = 34.

For angle R, the adjacent side is QR and the hypotenuse is PR, so

cos R = QR / PR = 16 / 34 = 8 / 17.