use the triangle shown on the right and the given information to solve the triangle. c = 6, b = 80°, find a…

Explanation:

Step1: Find angle A

In a right - triangle, the sum of the interior angles is 180°. Since one angle is 90° and B = 80°, then A=180° - 90° - 80° = 10°.

Step2: Find side a

We know that $\sin A=\frac{a}{c}$. Given c = 6 and A = 10°, then $a = c\sin A=6\times\sin10^{\circ}\approx6\times0.1736 = 1.0416$.

Step3: Find side b

We know that $\cos A=\frac{b}{c}$. Given c = 6 and A = 10°, then $b = c\cos A=6\times\cos10^{\circ}\approx6\times0.9848 = 5.9088$.

Answer:

$A = 10^{\circ},a\approx1.04,b\approx5.91$