Question

1. the angle of depression from the top of a cruise ship to the top of a sailboat is 22°. sitting above water, the cruise ship is 236 feet tall while the sailboat is 27 feet tall. find the distance between the cruise ship and the sailboat.

Explanation:

Step1: Calculate the height difference

The height difference \(h\) between the two ships is \(h = 236 - 27=209\) feet.

Step2: Use the tangent function

Let the distance between the two ships be \(d\). We know that \(\tan\theta=\frac{h}{d}\), where \(\theta = 22^{\circ}\) and \(h = 209\). So \(d=\frac{h}{\tan\theta}\).
Since \(\tan(22^{\circ})\approx0.404\), then \(d=\frac{209}{0.404}\)

Step3: Calculate the value of \(d\)

\(d=\frac{209}{0.404}\approx517.33\)

Answer:

The distance between the cruise ship and the sailboat is approximately \(517.33\) feet.