How do you solve the triangle given A=28, a=8.5, b=7.2?

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Answer 1 · 2018-05-05T03:59:37

$color(brown)(c = 14.16, hat B = 23.43^@, hat C = 128.57^@, A_t = 23.92 " sq units"$

$"As per Law of Sines ", a / sin A = b / sin B = c / sin C$

$hat A = 28^@, ab = 8.5, b = 7.2$

$8.5 / sin 28 = 7.2 / sin B$

$sin B = (7.2 * sin 28) / 8.5 = 0.3977$

$hat B = sin ^ -1 0.3977 = 23.43^@$

$hat C = 180 - 28 - 23.43= 128.57^@$

$c = (a * sin C) / sin A = (8.5 * sin 128.57) / sin 28 = 14.16$

$"Area of Triangle " = A_t = (1/2) a b sin C$

$A_t = (1/2) * 7.2 * 8.5 * sin 128.57 = 23.92 " sq units"$