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

Step2: Find side a

We know that $\tan B=\frac{b}{a}$. So $a=\frac{b}{\tan B}$. Substituting $B = 15.1^{\circ}$ and $b = 36.5$, we have $\tan(15.1^{\circ})\approx0.2707$, and $a=\frac{36.5}{0.2707}\approx134.84$.

Step3: Find side c

We know that $\sin B=\frac{b}{c}$. So $c=\frac{b}{\sin B}$. Substituting $B = 15.1^{\circ}$ and $b = 36.5$, we have $\sin(15.1^{\circ})\approx0.2598$, and $c=\frac{36.5}{0.2598}\approx140.49$.

Answer:

$a\approx134.84$
$c\approx140.49$