Question

find the distance from point b to point c. enter as a decimal rounded to the nearest tenth. bc = ? mi

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 66^{\circ}\), the adjacent side \(AB = 5\) mi, and the opposite side is \(BC\). So, \(\tan(66^{\circ})=\frac{BC}{5}\).

Step2: Solve for \(BC\)

Multiply both sides of the equation \(\tan(66^{\circ})=\frac{BC}{5}\) by \(5\). We get \(BC = 5\times\tan(66^{\circ})\).
Since \(\tan(66^{\circ})\approx2.246\), then \(BC = 5\times2.246=11.23\).

Answer:

\(11.2\) mi