Question

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.”

$A=100,a=5,c=2$

Short answer

No triangle exists

Step-by-step solution

Step 1. Given information   

The given data from the graph is$A={100}^{°},a=5,c=2$

Step 2. Find angle C

Applying the law of sines

$$\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin 100}{5}=\frac{\sin B}{b}=\frac{\sin C}{2} \\ \frac{\sin 100}{5}=\frac{\sin C}{2} \\ \sin C=2\frac{\sin 100}{5} \\ \sin C=0.39 \\ C=23.2^{\circ } \end{gathered}$$

Step 3. Find angle b

By Pythagoras theorem, $c^2=a^2+b^2$

$$\begin{gathered} c^2=a^2+b^2 \\ 4=25+b^2 \\ {b}^2=-21 \\ b=\sqrt{-21} \end{gathered}$$

Which is not possible