Answer
$$A=35.3°$$
$$B=54.7°$$
Work Step by Step
Find angle A.
We can use the trigonometric function for tangent to find angle A.
$tan A=\frac{a}{b}$
$tan A=\frac{36 m}{50.9m}$
$tan A=0.7072$
Now we solve for A by multiplying both sides of the equation by the inverse tangent.
So,
$tan^{-1}(tan A) = tan^{-1}(0.7072)$
$A = tan^{-1}(0.7072)$
$A=35.3°$
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
$B=90°-A$
$B=90°-35.3°$
$B=54.7°$
