Question

question #
note: triangle may not be drawn to scale. suppose c = 14 and a = 30 degrees. find: a =
b =
b = degrees
give all answers to at least one decimal place. give angles in degrees add work > next question

Explanation:

Step1: Find side a using sine - rule

In a right - triangle, $\sin A=\frac{a}{c}$. Given $c = 14$ and $A = 30^{\circ}$, then $a=c\sin A$. Substituting the values, we have $a = 14\times\sin30^{\circ}=14\times\frac{1}{2}=7$.

Step2: Find side b using cosine - rule

$\cos A=\frac{b}{c}$. Given $c = 14$ and $A = 30^{\circ}$, then $b=c\cos A$. So $b = 14\times\cos30^{\circ}=14\times\frac{\sqrt{3}}{2}=7\sqrt{3}\approx12.1$.

Step3: Find angle B

In a right - triangle, $A + B=90^{\circ}$. Given $A = 30^{\circ}$, then $B=90^{\circ}-A$. So $B = 90 - 30=60^{\circ}$.

Answer:

$a = 7$
$b\approx12.1$
$B = 60$