Question

1. the top of a lighthouse is 100 m above sea level. the angle of elevation from the deck of the sailboat to the top of the lighthouse is 28°. calculate the distance between the sailboat and the lighthouse.

Explanation:

Step1: Set up tangent - ratio

We have a right - triangle where the height of the lighthouse (opposite side) is 100 m and the angle of elevation is 28°. Let the distance between the sailboat and the lighthouse (adjacent side) be \(x\). The tangent of an angle in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan28^{\circ}=\frac{100}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x = \frac{100}{\tan28^{\circ}}\). Since \(\tan28^{\circ}\approx0.5317\), then \(x=\frac{100}{0.5317}\approx188.08\) m.

Answer:

Approximately 188.08 m