Question

solve the right - triangle. round your answers to the nearest tenth.

Explanation:

Step1: Find angle B

The sum of angles in a triangle is 180°. In a right - triangle, one angle is 90°. Given one non - right angle A = 47°.
$B=180^{\circ}-90^{\circ}-47^{\circ}=43^{\circ}$

Step2: Find side a

We know the adjacent side to angle A is 27. We use the tangent function $\tan(A)=\frac{a}{27}$. Since $A = 47^{\circ}$, $\tan(47^{\circ})\approx1.0724$. Then $a = 27\times\tan(47^{\circ})\approx27\times1.0724 = 28.9548\approx29.0$

Step3: Find side c

We use the cosine function $\cos(A)=\frac{27}{c}$. Since $A = 47^{\circ}$, $\cos(47^{\circ})\approx0.6820$. Then $c=\frac{27}{\cos(47^{\circ})}=\frac{27}{0.6820}\approx39.6$

Answer:

$c = 39.6$, $a = 29.0$, $B = 43^{\circ}$