Answer: option c.
Step-by-step explanation:
To find AB you can use the Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]
Where "c" is the hypotenuse and "a" and "b" are the legs of the triangle.
In this case:
[tex]c=AB\\a=BC=7.50mi\\b=AC=11.43mi[/tex]
Substituting values and solving for AB, we get:
[tex]AB^2=(7.50mi)^2+(11.43mi)^2\\\\AB=\sqrt{(7.50mi)^2+(11.43mi)^2}\\\\AB=13.7mi[/tex]
To find ∠B you can use the Arctangent. Then, this is:
[tex]\angle B=arctan(\frac{11.43mi}{7.50m})=56.7\°[/tex]
Since the sum of the interior angles of a triangle is 180 degrees, we know that the ∠A is:
[tex]\angle A=180\°-56.7\°-90\°\\\\\angle A=33.3\°[/tex]
