Question

Solve each triangle.

Short answer

The solution is$C=95°,a\approx 2.8,b\approx 2.6$

Step-by-step solution

Step 1. Given information 

Step 2. Calculation 

We know,

$A+B+C=180°$

$45°+40°+C=180°$

$C=95°$

Now use Law of Sines -

$\frac{\sin A}{a}=\frac{\sin C}{c}$ and localid="1646914101591" $\frac{\sin B}{b}=\frac{\sin C}{c}$

$\frac{\sin 45°}{a}=\frac{\sin 95°}{4}$ localid="1646914347701" $\frac{\sin 40°}{b}=\frac{\sin 95°}{4}$

$\frac{4\sin 45°}{\sin 95°}=a$ $\frac{4\sin 40°}{\sin 95°}=b$

$2.8\approx a$ $2.6\approx b$