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 = 58.5° (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 side a using tangent

Since $\tan A=\frac{a}{b}$, then $a = b\tan A$. Substituting $A = 31.5^{\circ}$ and $b = 45$, we have $a=45\times\tan(31.5^{\circ})$.
$a = 45\times0.619778\approx27.89$

Step2: Find side c using cosine

Since $\cos A=\frac{b}{c}$, then $c=\frac{b}{\cos A}$. Substituting $A = 31.5^{\circ}$ and $b = 45$, we get $c=\frac{45}{\cos(31.5^{\circ})}$.
$c=\frac{45}{0.859404}\approx52.36$

Answer:

$a = 27.89$
$c = 52.36$