Question

watch the video and then solve the problem given below. click here to watch the video. solve the right triangle shown in the figure. b = 15.1°, b = 36.5 a = 74.9° (round to the nearest tenth as needed.) a ≈ 135.03 (round to the nearest hundredth as needed.) c ≈ 140.55 (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 $A = 90^{\circ}-B$.
$A=90^{\circ}- 15.1^{\circ}=74.9^{\circ}$

Step2: Find side a

We know that $\tan B=\frac{b}{a}$, so $a=\frac{b}{\tan B}$.
$a = \frac{36.5}{\tan(15.1^{\circ})}\approx\frac{36.5}{0.2703}\approx135.03$

Step3: Find side c

We know that $\sin B=\frac{b}{c}$, so $c=\frac{b}{\sin B}$.
$c=\frac{36.5}{\sin(15.1^{\circ})}\approx\frac{36.5}{0.2607}\approx140.55$

Answer:

$A = 74.9^{\circ}$, $a\approx135.03$, $c\approx140.55$