Question

Please select the best answer from the choices provide

Answer 1

Answer: Option C.

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)=(opposite)/(adjacent)`

Where:

`opposite=7.50\\adjacent=11.43`

Then:

`tan^(-1)(A)=(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.