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 = 34.3° b = 44 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, $B = 90^{\circ}-A$.
$B=90^{\circ}- 34.3^{\circ}=55.7^{\circ}$

Step2: Find side a

We know that $\tan A=\frac{a}{b}$. So, $a = b\tan A$.
Substitute $A = 34.3^{\circ}$ and $b = 44$ into the formula:
$a=44\times\tan(34.3^{\circ})\approx44\times0.7097\approx31.23$

Step3: Find side c

We know that $\cos A=\frac{b}{c}$. So, $c=\frac{b}{\cos A}$.
Substitute $A = 34.3^{\circ}$ and $b = 44$ into the formula:
$c=\frac{44}{\cos(34.3^{\circ})}\approx\frac{44}{0.8256}\approx53.30$

Answer:

$B = 55.7^{\circ}$
$a\approx31.23$
$c\approx53.30$