Question

Please select the best answer from the choices provide

Answer 1

Answer: Option C.

Step-by-step explanation:

1. Apply the Pythagorean Theorem to calculate AB:

$AB=\sqrt{BC^{2}+AC^{2}}\\AB=\sqrt{(7.50mi)^{2}+(11.43mi)^{2}}\\AB=13.7mi$

2. Now, you can calculate the angle ∠A as following:

$tan^{-1}(\alpha)=\frac{opposite}{adjacent}$

Where:

$opposite=7.50\\adjacent=11.43$

Then:

$tan^{-1}(A)=\frac{7.50}{11.43}$

∠$A=33.3$°

3. The sum of the interior angles of a triangle is 180°. So, you can find the angle ∠B as following:

∠$B=180$°-∠A-∠C

∠$B=180$°-$33.3$°-$90$°=$56.7$°

4. Therefore, the answer is the option c.