Use the Law of Sines to solve the triangle with the following angles and side.

Question

A = 120 degrees

B = 45 degrees

c= 16

Round your answer to two decimal places.

Answer 1

C= 180-120-45 = 25 degrees, c=16

sinC/c = .423/16 = 0.0264 = sinA/a = sinB/b

a =sin120/.0264 = .866/.0264= 32.80

b = sin45/.0264 = .707/.0264 = 26.78

C is the smallest angle, and the side opposite it will be the smallest length

A is the largest angle and the side opposite it, a, will be the longest side

B is the middle angle, and b will be the middle length of the triangle

Answer 2

angle C = 180 - 120 - 45 = 15

sin (C) = sin (B)

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c b

we have c = 16, B = 45 and C = 15, so can solve for b

sin(C) = sin (A)

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c a

where have c = 16, C = 15 and A = 120, so can solve for A.