How do you solve the triangle given #triangleRST, r=38, s=28, t=18#?

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Answer 1 · 2018-02-26T09:52:22

#color(brown)(hat R = 109.47^@, hat S = 44^@, hat T = 26.53^@#

#color(blue)(r = 38, s = 28, t = 18#

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Given three sides.

#A_t = sqrt (p (p-r) (p-s) (p - t))# where a,b,c are the three sides and p the semi perimeter of the triangle.

#p= (r + s + t) / 2 =(38 + 28 + 18) / 2 = 42#

#A_t = sqrt(42 (42-38) (42 - 28) (42 - 18)) = 237.59#

Having known the area, we can find one angle using area formula

#A_t = (1/2) r s sin T#

#sin T = (237.59 * 2) / (38 * 28) = 0.4466#

#hat T = sin ^-1 0. 4466 = 26.53^@#

Similarly, #hat S = sin ^-1 ((237.59 * 2)/ (38 * 18)) = 44^@#

#hat R = 180 - 26.53 - 44 = 109.47^@#