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 = 51.2 ° (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 $B = 90^{\circ}-A$. Given $A = 38.8^{\circ}$, then $B=90^{\circ}-38.8^{\circ}=51.2^{\circ}$.

Step2: Find side a

We know that $\tan A=\frac{a}{b}$. Given $A = 38.8^{\circ}$ and $b = 25$, then $a=b\tan A$. Substituting the values, $a = 25\times\tan(38.8^{\circ})$. Using a calculator, $a=25\times0.8078\approx20.19$.

Step3: Find side c

We know that $\cos A=\frac{b}{c}$, so $c=\frac{b}{\cos A}$. Given $A = 38.8^{\circ}$ and $b = 25$, then $c=\frac{25}{\cos(38.8^{\circ})}$. Using a calculator, $c=\frac{25}{0.7809}\approx32.02$.

Answer:

$a = 20.19$
$c = 32.02$