Question

solve the right triangle shown in the figure to the right. round lengths to two decimal places and express angles to the nearest tenth of a degree. a = 33.2° b = 32 b = (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 B

In a right - triangle, the sum of the two non - right angles is 90°. So, $B = 90^{\circ}-A$.
$B=90 - 33.2=56.8^{\circ}$

Step2: Find side a

We know that $\tan A=\frac{a}{b}$. So, $a = b\times\tan A$.
$a = 32\times\tan(33.2^{\circ})$
$a\approx32\times0.6577\approx21.05$

Step3: Find side c

We know that $\cos A=\frac{b}{c}$. So, $c=\frac{b}{\cos A}$.
$c=\frac{32}{\cos(33.2^{\circ})}$
$c=\frac{32}{0.8346}\approx38.34$

Answer:

$B = 56.8^{\circ}$
$a\approx21.05$
$c\approx38.34$