Question

solve the right triangle shown in the figure. b = 17.3°, b = 37.5 a = □° (round to the nearest tenth as needed.) a ≈ □ (round to the nearest hundredth as needed.) c ≈ □ (round to the nearest hundredth as needed.)

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the two non - right angles is 90°. So $A = 90^{\circ}-B$.
$A=90^{\circ}- 17.3^{\circ}=72.7^{\circ}$

Step2: Find side a

We know that $\tan B=\frac{b}{a}$. So $a = \frac{b}{\tan B}$.
$a=\frac{37.5}{\tan(17.3^{\circ})}\approx\frac{37.5}{0.3145}\approx119.24$

Step3: Find side c

We know that $\sin B=\frac{b}{c}$. So $c=\frac{b}{\sin B}$.
$c=\frac{37.5}{\sin(17.3^{\circ})}\approx\frac{37.5}{0.2974}\approx126.09$

Answer:

$A = 72.7^{\circ}$
$a\approx119.24$
$c\approx126.09$