From the top of a 189-ft lighthouse, the angle of depression to a ship in the ocean is 25°. How far is the ship from the base of the lighthouse? 

To find the distance between the ship and the base of the lighthouse, we can use basic trigonometry. Since we have an angle of depression and the height of the lighthouse, this problem forms a right triangle.

- The height of the lighthouse is the opposite side of the triangle.
- The distance from the ship to the base of the lighthouse is the adjacent side.
- The angle of depression is \( 25^\circ \).

We will use the tangent function because it relates the opposite side (height of the lighthouse) to the adjacent side (distance to the ship):

\[
\tan(\theta) = \frac{{\text{opposite}}}{{\text{adjacent}}}
\]

Substitute the known values:

\[
\tan(25^\circ) = \frac{{189}}{{d}}
\]

Where \( d \) is the distance from the base of the lighthouse to the ship. Solving for \( d \):

\[
d = \frac{{189}}{{\tan(25^\circ)}}
\]

Now let's calculate that.

It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still solve it manually using the formula we set up earlier:

\[
d = \frac{189}{\tan(25^\circ)}
\]

Now, if you'd like, I can guide you through calculating it with a calculator or answer any other questions.

Here are 5 related questions:
1. What is the difference between an angle of elevation and an angle of depression?
2. How do we determine which trigonometric function to use in a right triangle problem?
3. How would the distance change if the angle of depression increased?
4. What if the lighthouse was taller? How would that affect the calculation?
5. How can you apply this method to other real-world problems involving right triangles?

**Tip:** Always make sure your calculator is in the correct mode (degrees or radians) when working with angles.

From the top of a 189-ft lighthouse, the angle of depression to a ship in the ocean is 25°. How far is the ship from the base of the lighthouse?

Learn how to calculate the distance from the base of a 189-ft lighthouse to a ship using the angle of depression (25°). This problem involves basic trigonometry, utilizing the tangent function to solve real-world right triangle problems. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation