Answer: Option C.
Step-by-step explanation:
1. Apply the Pythagorean Theorem to calculate AB:
[tex]AB=\sqrt{BC^{2}+AC^{2}}\\AB=\sqrt{(7.50mi)^{2}+(11.43mi)^{2}}\\AB=13.7mi[/tex]
2. Now, you can calculate the angle ∠A as following:
[tex]tan^{-1}(\alpha)=\frac{opposite}{adjacent}[/tex]
Where:
[tex]opposite=7.50\\adjacent=11.43[/tex]
Then:
[tex]tan^{-1}(A)=\frac{7.50}{11.43}[/tex]
∠[tex]A=33.3[/tex]°
3. The sum of the interior angles of a triangle is 180°. So, you can find the angle ∠B as following:
∠[tex]B=180[/tex]°-∠A-∠C
∠[tex]B=180[/tex]°-[tex]33.3[/tex]°-[tex]90[/tex]°=[tex]56.7[/tex]°
4. Therefore, the answer is the option c.
