Answer to Question #142863 in Trigonometry for Raffy

Question

Solve the following triangles. Identify the case # in each given
triangle.

1.) given parts:

c= 21.37 B= 37°6' C= 42°38'

Answer 1

c=21.37

B= 37°6'

C= 42°38'

B+C = 79°44'

By angle sum property of triangle

A+B+C = 180°

So A = 180° - (B+C) = 180° - 79°44' = 100°16'

By Sin rule of triangle

$\frac {a}{sinA}=\frac {b}{sinB}=\frac {c}{sinC}$

$\frac {a}{sin100°16'}=\frac {b}{sin37°6'}=\frac {21.37}{sin42°38'}$

$\frac {a}{0.98398889}=\frac {b}{0.60320799}=$ 31.5515586

Therefore, a = 31.5515586*0.98398889 = 31.04638312

= 31.05 [correct upto two places of decimal]

b = 31.5515586*0.60320799

= 19.03215224

= 19.03 [correct upto two places of decimal]

So solution is

a= 31.05

b= 19.03

A= 100°16'

along with c = 21.37, B=37°6', C=42°38'