Question

what are the exact values of a and b?

o a = 7/2, b = 7√3

o a = 7/2, b = 7√2/2

o a = 7√3/2, b = 7/2

o a = 7/2, b = 7√3/2

Explanation:

Step1: Use sine function for side a

In right - triangle \(ABC\), \(\sin A=\frac{a}{AB}\). Given \(A = 30^{\circ}\) and \(AB = 7\). Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(a = AB\times\sin A=7\times\frac{1}{2}=\frac{7}{2}\).

Step2: Use cosine function for side b

\(\cos A=\frac{b}{AB}\). Given \(A = 30^{\circ}\) and \(AB = 7\). Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(b = AB\times\cos A=7\times\frac{\sqrt{3}}{2}=\frac{7\sqrt{3}}{2}\)

Answer:

\(a=\frac{7}{2},b = \frac{7\sqrt{3}}{2}\) (the last option)