Question

7.1, 7.2 apps
score: 3/8 answered: 3/8
question 8
from the top of a 193-ft lighthouse, the angle of depression to a ship in the ocean is 28°. how far is the ship from the base of the lighthouse?
distance = feet
report answer accurate to 2 decimal places.
question help: message instructor

Explanation:

Step1: Relate angle of depression and trigonometric ratio

The angle of depression is equal to the angle of elevation from the ship to the top of the lighthouse. Let the distance from the ship to the base of the lighthouse be \(x\). We know the height of the lighthouse \(h = 193\) ft and the angle \(\theta=28^{\circ}\). Using the tangent ratio \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), here \(\tan(28^{\circ})=\frac{193}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(x=\frac{193}{\tan(28^{\circ})}\). Since \(\tan(28^{\circ})\approx0.5317\), then \(x = \frac{193}{0.5317}\).

$$x=\frac{193}{0.5317}\approx362.99$$

Answer:

\(362.99\)