Answer
$C=120°$
$b\approx1.06$
$c\approx2.69$
Work Step by Step
Sketch the triangle using the given measurements.
Refer to the attached image below.
The sum of the three angles inside a triangle is $180^o$ so $A+B+C=180°$
Here,
$A=40°$
$B=20°$
$a=2$
Therefore,
$C=180°−40°−20°\\
C=120°$
Now, by applying the Law of Sines we can calculate the values of the remaining two sides:
$$\dfrac{\sin(A)}{a}=\dfrac{\sin(B)}{b}=\dfrac{\sin(C)}{c}$$
We know one side of the equation, which is:
$$\dfrac{\sin(A)}{a}=\dfrac{\sin(40°)}{2}$$
First, we calculate for $b$:
$$\dfrac{\sin(B)}{b}=\dfrac{\sin(A)}{a}\\
\dfrac{\sin(20°)}{b}=\dfrac{\sin40^o}{2}$$
Cross-multiply, then isolate $b$ to obtain:
$$b\cdot\sin40^o=2\cdot \sin20^o\\
b=\dfrac{2\cdot \sin20^o}{\sin40^o}\\
b\approx1.06
$$
Next, we calculate for $c$:
$$\dfrac{\sin(C)}{c}=\dfrac{\sin(A)}{a}\\
\frac{\sin(120°)}{c}=\dfrac{\sin40°}{2}$$
Cross-multiply, then isolate $c$ to obtain:
$$c\cdot \sin40°=2\cdot \sin120°\\
c=\dfrac{2\cdot \sin120°}{\sin40°}\\
c\approx 2.69$$
