Question

solve the right triangle.
a = (round to four decimal places as needed.)
a = cm (round to three decimal places as needed.)
c = cm (round to three decimal places as needed.)

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the two non - right angles is 90°. So $A = 90^{\circ}-B$. Given $B = 44.0898^{\circ}$, then $A=90^{\circ}- 44.0898^{\circ}=45.9102^{\circ}$.

Step2: Find side a

We know that $\tan B=\frac{b}{a}$, where $b = 58.859$ cm. So $a=\frac{b}{\tan B}$. Substituting $b = 58.859$ cm and $B = 44.0898^{\circ}$, we have $a=\frac{58.859}{\tan(44.0898^{\circ})}\approx60.494$ cm.

Step3: Find side c

We know that $\sin B=\frac{b}{c}$, so $c=\frac{b}{\sin B}$. Substituting $b = 58.859$ cm and $B = 44.0898^{\circ}$, we get $c=\frac{58.859}{\sin(44.0898^{\circ})}\approx84.247$ cm.

Answer:

$A = 45.9102^{\circ}$
$a\approx60.494$ cm
$c\approx84.247$ cm