Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both.

Question

A = 23° 17',  a = 9.5,  b = 22

Answer 1

Convert units of A.

A =23° 17'=23°+(17/60) =23.28°

Write the sine rule

a/sin(A) = b/sin(B) = c/sin (C)

a/sin(A) = b/sin(B)

9.5/sin(23.28) = 22/sin(B)

sin(B) =22*sin(23.28)/9.5

        =0.915

B =66.24° =66°14'

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In triangle, sum of three angles is 180

A+B+C =180

23.28+66.24+C =180

C =90.48° =90°29'

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b/sin(B) = c/sin (C)

22/sin(66.24) = c/sin(90.48)

c =22*sin(90.48)/sin(66.24)

    =24.04