How do you solve the triangle given r = 15, t = 8, angle S = 125º?

1 Answer
Jun 26, 2018

color(maroon)(s = 20.66, hat R = 36.49^@, hat T = 18.51^@

Explanation:

Law of cosines s^2 = r^2 + t^2 - 2 r t cos S

r = 15, t = 8, hat S = 125^@

s^2 = 15^2 + 8^2 - (2 * 15 * 8 * cos (125)) = 426.66

s = sqrt 426.66 ~~ 20.66

Law of Sines sin S / s =sin R / r = sin T / t

sin R = (r sin S) / s = (15 * sin (125)) / 20.66 = 0.5947

hat R = sin ^-1 (0.5947) = 36.49^@

hat T = 180 - 125 - 36.49 = 18.51^@