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

1 Answer
Jun 26, 2018

Answer:

#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^@#