How do you find the measure of each of the angles of a triangle given the measurements of the sides are 9, 10, 15?

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Answer 1 · 2018-02-26T15:16:45

#color(blue)(hat A = 35.58^@, hat B = 40.27^@, hat C = 104.15^@)#

#a = 9, b = 10, c = 15#

enter image source here

Applying law of Cosines,

#c^2 = a^2 + b^2 - (2 a b cos C)#

#cos C = (a^2 + b^^2 - c^2) / (2 a b)#

#cos C = (9^2 + 10^2 - 15^2) / (2 * 9 * 10) = - 0.2444#

#hat C = cos ^-1 (-0.2444) = 104.15^@#

Applying law of sines,

enter image source here
#hat A = sin ^-1 ((sin C * a) / c) = sin ^-1 (sin 104.15 * 9) / 15 = 35.58^@#

#hat B = 180 - 104.15 - 35.58 = 40.27^@#