Question

Solve each triangle.

$a=12,b=13,c=5$

Short answer

The solution is$A\approx 67.4°,B=90°,C\approx 22.6°$.

Step-by-step solution

Step 1. Given information 

$a=12,b=13,c=5$

Step 2. Calculation 

For A:

$\cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{169+25-144}{2·13·5}=\frac{5}{13}$

$A={\cos }^{-1}\frac{5}{13}\approx 67.4°$

For$B$:

$\cos B=\frac{a^2+c^2-b^2}{2ac}=\frac{144+25-169}{2·12·5}=\frac{0}{120}=0$

$B={\cos }^{-1}\left(0\right)=90°$

Since we know $A$and $B$,

$C=180°-A-B$

$\approx 180°-67.4°-90°$

$\approx 22.6°$