Question

score: 3/8 answered: 4/8 question 8 score on last try: 0 of 1 pts. see details for more. get a similar question you can retry this question below from the top of a 188-ft lighthouse, the angle of depression to a ship in the ocean is 20°. how far is the ship from the base of the lighthouse? distance = 516.65 × feet report answer accurate to 2 decimal places. question help: message instructor

Explanation:

Step1: Use the tangent function

The angle of depression is \(20^{\circ}\), and the height of the lighthouse (opposite side) is \(h = 188\) ft. Let the distance from the base of the lighthouse to the ship (adjacent side) be \(x\). Since the angle of depression is equal to the angle of elevation from the ship to the top of the lighthouse, we have \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 20^{\circ}\) and \(\tan(20^{\circ})=\frac{188}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation \(x=\frac{188}{\tan(20^{\circ})}\). We know that \(\tan(20^{\circ})\approx0.3640\). Then \(x=\frac{188}{0.3640}\).

$$x=\frac{188}{0.3640}\approx516.48$$

Answer:

\(516.48\)