To find:
The angle A and angle B and side c.
Solution:
Given a = 18.5 and b = 14.
if we take tangent of angle A, then
[tex]\begin{gathered} \tan A=\frac{a}{b} \\ \Rightarrow\tan A=\frac{18.5}{14.2} \\ \Rightarrow A=\tan^{-1}(\frac{18.5}{14.2}) \\ \Rightarrow A=52.49\text{ degrees} \end{gathered}[/tex]
It is known that the sum of all three angles is 180 degrees. So,
[tex]\begin{gathered} A+B+C=180 \\ 52.49+B+90=180 \\ B=37.51\text{ degrees} \end{gathered}[/tex]
Now, we use Pythagoras theorem to find the value of c:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=14.2^2+18.5^2 \\ c^2=201.64+342.25 \\ c^2=543.89 \\ c=23.32 \end{gathered}[/tex]
Thus, angle A = 52.49 degrees, angle B = 37.51 degrees and c = 23.32.
