Respuesta :
Here's a breakdown of how to solve this problem, presented clearly for an exam setting:
**Problem:**
From the top of a 230-ft lighthouse, the angle of depression to a ship in the ocean is 16°. How far is the ship from the base of the lighthouse?
**Solution:**
1. **Diagram:** Draw a right triangle.
* Vertical side: Lighthouse (height = 230 ft)
* Horizontal side: Distance from ship to base of lighthouse (this is what we want to find)
* Hypotenuse: Line of sight from the top of the lighthouse to the ship
* Angle of depression: 16° at the top of the lighthouse
2. **Trigonometry:**
* We have the opposite side (230 ft) and need to find the adjacent side.
* Use the tangent function: tan(angle) = opposite/adjacent
3. **Calculations:**
* tan(16°) = 230 ft / distance
* distance = 230 ft / tan(16°)
* distance ≈ 801.4 ft
**Answer:**
The ship is approximately 801.4 feet from the base of the lighthouse.
**Important Notes (for showing your understanding):**
* The angle of depression is the angle between the horizontal line of sight and the line going down to the object.
* Make sure your calculator is in degree mode for trigonometric calculations.
