Question

college trigonometry mac 1114 202601 10191 question completed: 3 of 12 my score: 3/12 pts (25%) save solve the right triangle abc, with c = 90°. b = 63.9°, b = 113 in. a = ° (simplify your answer. type an integer or a decimal. round to the nearest tenth as needed.) a = in. (simplify your answer. type an integer or a decimal. round to the nearest tenth as needed.) c = in. (simplify your answer. type a whole number.)

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the interior angles is 180°. Since C = 90° and B = 63.9°, then A=180° - 90° - 63.9°.
$A = 26.1^{\circ}$

Step2: Find side a

We know that $\tan B=\frac{b}{a}$. So, $a=\frac{b}{\tan B}$. Substituting b = 113 in and B = 63.9°, we have $a=\frac{113}{\tan(63.9^{\circ})}$.
$a=\frac{113}{2.0447}\approx55.3$ in

Step3: Find side c

We know that $\sin B=\frac{b}{c}$. So, $c = \frac{b}{\sin B}$. Substituting b = 113 in and B = 63.9°, we have $c=\frac{113}{\sin(63.9^{\circ})}$.
$c=\frac{113}{0.8976}\approx126$ in

Answer:

$A = 26.1^{\circ}$
$a = 55.3$ in
$c = 126$ in