We have to solve the right triangle.
We know two of the sides: a = 13.2 and b = 17.7.
This are the two legs, and we have to find c, the hypotenuse and A and B, the two non-right angles.
We can calculate c as:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=13.2^2+17.7^2 \\ c^2=174.24+313.29 \\ c^2=487.53 \\ c=\sqrt{487.53} \\ c\approx22.1 \end{gathered}[/tex]We can now find the angles using trigonometric ratios.
We can find A as:
[tex]\begin{gathered} \tan A=\frac{Opposite}{Adjacent}=\frac{a}{b}=\frac{13.2}{17.7}\approx0.7458 \\ \\ A\approx\arctan(0.7458)\approx36.7\degree \end{gathered}[/tex]We can find B as:
[tex]\begin{gathered} \tan B=\frac{b}{a}=\frac{17.7}{13.2}\approx1.3409 \\ \\ B\approx\arctan(1.3409)\approx53.3\degree \end{gathered}[/tex]Answer:
A = 36.7°, B = 53.3°, c = 22.1 [Option C]
