solve the right triangle.\na = (round to four decimal places as needed.)\na = cm (round to three decimal…

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the two non - right angles is 90°. So $A = 90^{\circ}-B$. $A=90^{\circ}- 38.0898^{\circ}=51.9102^{\circ}$

Step2: Find side a

We know that $\tan B=\frac{b}{a}$, where $b = 55.855$ cm. So $a=\frac{b}{\tan B}$. $a=\frac{55.855}{\tan(38.0898^{\circ})}\approx71.094$ cm

Step3: Find side c

We know that $\sin B=\frac{b}{c}$, so $c=\frac{b}{\sin B}$. $c=\frac{55.855}{\sin(38.0898^{\circ})}\approx90.447$ cm

Answer:

$A = 51.9102^{\circ}$ $a\approx71.094$ cm $c\approx90.447$ cm