Question

solve each of the following right triangles for all missing angle sizes and all missing side lengths in the triangles shown below. round answers to the nearest tenth. b. ∠b = 68.3°, a = 417

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the two non - right angles is 90°. Given $\angle B = 68.3^{\circ}$, then $\angle A=90^{\circ}-\angle B$.
$\angle A = 90^{\circ}-68.3^{\circ}=21.7^{\circ}$

Step2: Find side b

We know that $\tan B=\frac{b}{a}$. Given $a = 417$ and $\angle B = 68.3^{\circ}$, then $b=a\tan B$.
$b = 417\times\tan(68.3^{\circ})\approx417\times2.475\approx1032.1$

Step3: Find side c

We know that $\cos B=\frac{a}{c}$, so $c=\frac{a}{\cos B}$.
$c=\frac{417}{\cos(68.3^{\circ})}\approx\frac{417}{0.371}\approx1124.0$

Answer:

$\angle A = 21.7^{\circ}$, $b\approx1032.1$, $c\approx1124.0$