Round answers to the nearest 10 th Irom the top of lighthouse 180 feet above sea level, the angle of depres sion to a ship in the ocean is 28 How far is the ship from the base of the light house?

Question

UpStudy AI · Accepted Answer

To determine how far the ship is from the base of the lighthouse, we'll use trigonometry, specifically the tangent function.

**Given:**
- **Height of the lighthouse (opposite side):** 180 feet
- **Angle of depression:** 28°

**Objective:**
- **Find the horizontal distance (adjacent side) from the base of the lighthouse to the ship.**

**Steps:**

1. **Understand the Relationship:**
   
   The angle of depression from the top of the lighthouse to the ship is equal to the angle between the horizontal ground and the line of sight to the ship. This forms a right-angled triangle where:
   
   $$
   \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
   $$
   
2. **Set Up the Equation:**
   
   $$
   \tan(28°) = \frac{180}{\text{Distance}}
   $$
   
   Let $$ \text{Distance} = x $$.
   
   $$
   x = \frac{180}{\tan(28°)}
   $$
   
3. **Calculate $$ \tan(28°) $$:**
   
   $$
   \tan(28°) \approx 0.5317
   $$
   
4. **Compute the Distance:**
   
   $$
   x = \frac{180}{0.5317} \approx 338.5 \text{ feet}
   $$
   
5. **Final Answer:**
   
   The ship is approximately **338.5 feet** from the base of the lighthouse.

**Conclusion:**

Using the tangent of the angle of depression and the height of the lighthouse, we've calculated that the ship is roughly **338.5 feet** away from the base of the lighthouse.
The ship is approximately 338.5 feet from the base of the lighthouse.

Round answers to the nearest 10 th Irom the top of lighthouse 180 feet above sea level, the angle of depres sion to a ship in the ocean is 28 How far is the ship from the base of the light house?

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Trigonometry Questions