Question

ab =
round your answer to the nearest hundredth.
10 of 30

Explanation:

Step1: Identify the trigonometric relation

In right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), \(\cos B=\frac{BC}{AB}\). Here, \(B = 50^{\circ}\) and \(BC = 2\).

Step2: Rearrange the formula to solve for \(AB\)

We know that \(\cos B=\frac{BC}{AB}\), so \(AB=\frac{BC}{\cos B}\).

Step3: Substitute the values

Substitute \(B = 50^{\circ}\) and \(BC = 2\) into the formula. \(\cos(50^{\circ})\approx0.6428\), then \(AB=\frac{2}{\cos(50^{\circ})}=\frac{2}{0.6428}\approx3.11\)

Answer:

\(3.11\)