Question

Find the cosine of ∠R.

image of a right triangle that has the following values, Angle S, Angle R, Angle Q, Line SR which has a length of 37, Line RQ which has an unknown length, and Line SQ which has a length of 35

Answer 1

SR = 37 is the longest side, so it’s the hypotenuse and the right angle is at Q. By Pythagoras,

RQ = sqrt(37^2 − 35^2) = sqrt(1369 − 1225) = sqrt(144) = 12.

For angle R, adjacent = RQ and hypotenuse = SR, so

cos ∠R = RQ / SR = 12 / 37.