Question

Find all solutions for a triangle with A=40 degrees , B=60 degrees and c = 20.

Answer 1

bc a triangle has a total of 180°, add angles A+B to get 40+60=100, so angle C must be 80° since 180°-100°= 80°

then use sohcahtoa

Answer 2

Answer:

The correct option is C) $\angle C=80\degree$ ,$a=13.1$ and $b=17.6$

Step-by-step explanation:

We need to calculate the solution for a triangle with $A=40\degrees \, B=60\degrees \ and \ c = 20$

Since, interior angle sum of triangle is 180°

$\angle A +\angle B +\angle C=180\degree$

$40\degree + 60\degree +\angle C=180\degree$

$100\degree +\angle C=180\degree$

Subtract both the sides by $100\degree$

$\angle C=180\degree-100\degree$

$\angle C=80\degree$

Sine law:-

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

by sine law

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

$\frac{\sin 40\degree}{a}=\frac{\sin 60\degree}{b}=\frac{\sin 80\degree}{20}$

Compare first and third fractions,

$\frac{\sin 40\degree}{a}=\frac{\sin 80\degree}{20}$

cross multiply

$\frac{20 \sin 40\degree}{\sin 80\degree}=a$

$\frac{20\times 0.642}{0.984}=a$

$a=13.1$

Compare second and third fractions,

$\frac{\sin 60\degree}{b}=\frac{\sin 80\degree}{20}$

cross multiply

$\frac{20 \sin 60\degree}{\sin 80\degree}=b$

$\frac{20\times 0.866}{0.984}=b$

$b=17.6$

Hence, the correct option is C) $\angle C=80\degree$ ,$a=13.1$ and $b=17.6$