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

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Answer 1 · 2018-06-26T06:43:03

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

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 $sin S / s =sin R / r = sin T / t$

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

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

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