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 = 38.8° b = 25 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, $B = 90^{\circ}-A$.
$B=90^{\circ}-38.8^{\circ}=51.2^{\circ}$

Step2: Find side a

We know that $\tan A=\frac{a}{b}$. Given $A = 38.8^{\circ}$ and $b = 25$. Then $a=b\tan A$.
$a = 25\times\tan(38.8^{\circ})\approx25\times0.8077 = 20.19$

Step3: Find side c

We know that $\cos A=\frac{b}{c}$. Then $c=\frac{b}{\cos A}$.
$c=\frac{25}{\cos(38.8^{\circ})}\approx\frac{25}{0.7809}\approx32.02$

Answer:

$B = 51.2^{\circ}$
$a\approx20.19$
$c\approx32.02$