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 = ° (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, $A = 90^{\circ}-B$.
$A=90^{\circ}- 15.1^{\circ}=74.9^{\circ}$

Step2: Find side a

We know that $\tan B=\frac{b}{a}$. So, $a = \frac{b}{\tan B}$.
$a=\frac{36.5}{\tan(15.1^{\circ})}$. Since $\tan(15.1^{\circ})\approx0.2703$, then $a=\frac{36.5}{0.2703}\approx135.03$.

Step3: Find side c

We know that $\sin B=\frac{b}{c}$. So, $c=\frac{b}{\sin B}$.
$c = \frac{36.5}{\sin(15.1^{\circ})}$. Since $\sin(15.1^{\circ})\approx0.2597$, then $c=\frac{36.5}{0.2597}\approx140.55$.

Answer:

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