Question

a) $a = \dfrac{1}{2}, b = \sqrt{3}$
b) $a = \dfrac{3}{2}, b = \dfrac{1}{2}$
c) $a = \sqrt{3}, b = 1$
d) $a = \dfrac{3}{2}, b = 1$

Explanation:

Step1: Find side $a$ (opposite 60°)

Use sine of 60°: $\sin60^\circ=\frac{a}{\text{hypotenuse}}$
$\sin60^\circ=\frac{\sqrt{3}}{2}=\frac{a}{2}$
$a=2\times\frac{\sqrt{3}}{2}=\sqrt{3}$

Step2: Find side $b$ (adjacent to 60°)

Use cosine of 60°: $\cos60^\circ=\frac{b}{\text{hypotenuse}}$
$\cos60^\circ=\frac{1}{2}=\frac{b}{2}$
$b=2\times\frac{1}{2}=1$

Answer:

C) $a=\sqrt{3}$, $b=1$