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 = 31.5° b = 45 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, $B = 90^{\circ}-A$.
$B=90^{\circ}-31.5^{\circ}=58.5^{\circ}$

Step2: Find side a

We know that $\tan A=\frac{a}{b}$. So, $a = b\tan A$.
$a = 45\times\tan(31.5^{\circ})$
$a\approx45\times0.619 = 27.86$

Step3: Find side c

We know that $\cos A=\frac{b}{c}$. So, $c=\frac{b}{\cos A}$.
$c=\frac{45}{\cos(31.5^{\circ})}$
$c=\frac{45}{0.853}\approx52.76$

Answer:

$B = 58.5^{\circ}$
$a\approx27.86$
$c\approx52.76$