Question

A= 82°, b=100°, c=78° Find: B

Answer 1

Solution;

From the law of Sine and cosine;

$\frac{sina}{sinB}=\frac{sinb}{sinB}=\frac{sinc}{sinC}+...$

Also;

$Cosa=cos(b)cos (c)+sin(b)sin(c)(cos A)$

By direct substitution;

$Cos (a)=cos100cos78+sin(100)sin(78)cos(82)$

Cos(a)=0.09796

Hence;

$a=84.38°$

Now;

$Sin(B)=\frac{sin(b)sin(A)}{sin(a)}$

$Sin(B)=\frac{sin(100)sin(82)}{sin(84.38}$

$Sin(B)=0.9799$

B=78.5°