Question

c. if the ship must be 50 m to the right of its current position from the lighthouse, what angle, a, should the captain direct the ship? round to the nearest degree.

Explanation:

Step1: Use the tangent function

In a right - triangle, the tangent of an angle \(A\) is given by \(\tan A=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(A\) is \(21.6\) m and the adjacent side is \(50\) m. So, \(\tan A=\frac{21.6}{50}\).

Step2: Calculate the value of \(\tan A\)

\(\tan A=\frac{21.6}{50}=0.432\).

Step3: Find the angle \(A\)

To find the angle \(A\), we use the inverse tangent function \(A = \tan^{-1}(0.432)\). Using a calculator, \(A=\tan^{-1}(0.432)\approx23^{\circ}\).

Answer:

\(23^{\circ}\)