How do you use law of sines to solve the triangle given C = 37°, a = 19, c = 8?

1 Answer
Kat
Nov 16, 2015

A=115.4^o
B=26.6^o
b=6.16

Explanation:

(sinA)/a=(sinB)/b=(sinC)/c

(sinA)/19=(sinC)/8
Multiply both sides by 19 and sinA=19(sin37)/8 which is sinA=1.429
The next step is to take the sin^-1 but you can not do an inverse of sin > 1 . We know that sin^-1(1)=90^o sin^-1(0.429)=25.4 90+25.4=115.4^o That's your angle A.

Angle B is 180-115.4-37=27.6^o

b/(sin27.6)=8/(sin37 so b=sin27.6(8/(sin37))
b=6.16

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