Answer
$$A=54.9°$$
$$B=35.1°$$
Work Step by Step
Find angle A.
We can use the trigonometric function for sine to find angle A.
$sin A=\frac{a}{c}$
$sin A=\frac{48.7cm}{59.5cm}$
$sin A=0.8185$
Now we solve for A by multiplying both sides of the equation by the inverse sine.
So,
$sin^{-1}(sin A) = sin^{-1}(0.8185)$
$A = sin^{-1}(0.8185)$
$A=54.9°$
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
$B=90°-A$
$B=90°-54.9°$
$B=35.1°$
