Question

solve for a and b.
a
14
30°
b
a = 14, b = 14√3
a = 28, b = 28√3
a = 14√2, b = 28
a = 28, b = 14√3

Explanation:

Step1: Use sine - function to find a

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$ and the opposite side to the $30^{\circ}$ angle is 14, and the hypotenuse is $a$. So, $\sin30^{\circ}=\frac{14}{a}$. Since $\sin30^{\circ}=\frac{1}{2}$, we have $\frac{1}{2}=\frac{14}{a}$, then $a = 28$.

Step2: Use cosine - function to find b

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the adjacent side to the $30^{\circ}$ angle is $b$ and the hypotenuse is $a = 28$. So, $\cos30^{\circ}=\frac{b}{a}$. Since $\cos30^{\circ}=\frac{\sqrt{3}}{2}$ and $a = 28$, then $b = 28\times\frac{\sqrt{3}}{2}=14\sqrt{3}$.

Answer:

$a = 28,b = 14\sqrt{3}$