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 = 37.9° b = 28 b = 52.1 ° (round to the nearest tenth as needed.) a = (round to the nearest hundredth as needed.) c = 35.49 (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 $B = 90^{\circ}-A$. Given $A = 37.9^{\circ}$, then $B=90 - 37.9=52.1^{\circ}$.

Step2: Find side a

We know that $\tan A=\frac{a}{b}$. Given $A = 37.9^{\circ}$ and $b = 28$, then $a=b\tan A$. Substituting the values, $a = 28\times\tan(37.9^{\circ})$. Using a calculator, $a=28\times0.7785\approx21.80$.

Step3: Find side c

We know that $\cos A=\frac{b}{c}$. Then $c=\frac{b}{\cos A}$. Given $A = 37.9^{\circ}$ and $b = 28$, $c=\frac{28}{\cos(37.9^{\circ})}$. Using a calculator, $c=\frac{28}{0.7889}\approx35.49$.

Answer:

$a = 21.80$