Answer
$$A=30.6°$$
$$B=59.4°$$
Work Step by Step
Find angle A.
We can use the trigonometric function for tangent to find angle A.
$tan A=\frac{a}{b}$
$tan A=\frac{58.44mi}{98.86mi}$
$tan A=0.5911$
Now we solve for A by multiplying both sides of the equation by the inverse tangent.
So,
$tan^{-1}(tan A) = tan^{-1}(0.5911)$
$A = tan^{-1}(0.5911)$
$A=30.6°$
Find angle B.
We know that in right triangles the sum of the acute angles is 90°.
So, $A+B=90°$
Solving for $B$, we get
$B=90°-A$
$B=90°-30.6°$
$B=59.4°$
