Question

Solve each triangle.

$b=4c=1,A=120°$

Short answer

The solution is$a\approx 4.6,B\approx 49.3°,C\approx 10.7°$

Step-by-step solution

Step 1. Given information 

$b=4c=1,A=120°$

Step 2. Calculation 

Use Law of Cosines -

$a^2=b^2+c^2-2bc\cos A$

$=16+1-2\times 4\times 1\cos 120°$

$=17-8\times -0.5$

$a\approx 4.6$

For C:

$c^2=a^2+b^2-2ab\cos C$

localid="1646894986845" $\cos C=\frac{a^2+b^2-c^2}{2ab}\approx \frac{21.16+16-1}{2\times 4.6\times 4}\approx \frac{36.16}{36.8}$

$C\approx {\cos }^{-1}\frac{36.16}{36.8}\approx 10.7°$

Since we know A and C,

$B=180°-120°-10.7°\approx 49.3°$