Question

Solve the triangle. B = 36°, a = 38, c = 18

Answer 1

Using cosine law.

b= sqrt(38^2 + 18^2 - 2(38)(18) Cos 36)
using calculator solve.
b = sqrt (1444 + 324 - 1106.75)
b = 25.75

Answer 2

Finishing the answer above:

B=36

a=38

c=18

b=25.7

a-b-c (SSS) {a^2=b^2+c^2-2ab(CosA) [Law of Cosines]

38^2=25.7^2+18^2-2(25.7)(18)(CosA)

1444=660.49+324-925.2(CosA)

1444=984.49-935.2(CosA)

459.51=-935.2(CosA)

-0.491349443969204=CosA

A=119.43

b-B-C (SAA) {(SinC)/c=(SinB/b)} [Law of Sines]

(SinC)/18=(Sin36)/25.7

(SinC)/18=0.022871021489979

SinC=0.411678386819631

C=24.31

A=119.43

B=36

C=24.31

a=38

b=25.7

c=18