https://file.aiquickdraw.com/mathbot/file/17265550264062b7yxcvo.jpg

Let's focus on solving the first problem visible in the image, which states:

"A 25 feet high lighthouse stands on the side of a hill. At a point 80 feet from the foot of the hill, the lighthouse subtends an angle of 17°. What angle does the side of the hill make with the lighthouse?"

To solve this problem, we can analyze it using trigonometry:

1. The lighthouse height is given as 25 feet.
2. The distance from the base is 80 feet.
3. The angle subtended by the lighthouse is 17°.

This problem involves a right triangle, where:
- The height of the lighthouse is the opposite side.
- The distance from the point is the adjacent side.
- The angle given (17°) is the angle at the point where the observation was made.

We can use the tangent function to find the unknown angle between the hill and the lighthouse. The equation will be:

\[
\tan(\theta) = \frac{\text{height of lighthouse}}{\text{distance from the foot of the hill}}
\]

Let's solve for \(\theta\). I'll calculate it now.The angle between the side of the hill and the lighthouse is approximately \( 17.35^\circ \).

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to explore:

1. What is the role of trigonometric functions in solving right triangle problems?
2. How can you calculate the distance to an object using angles and one side length?
3. Can the sine or cosine function be used in this problem instead of the tangent?
4. How does changing the height of the lighthouse affect the subtended angle?
5. What other real-world applications can you solve with trigonometry?

**Tip:** When working with angles, always make sure your calculator is in the correct mode (degrees or radians) to avoid errors in calculations.

A 25 feet high lighthouse stands on the side of a hill. At a point 80 feet from the foot of the hill, the lighthouse subtends an angle of 17°. What angle does the side of the hill make with the lighthouse?

Learn how to calculate the angle between a hill and a lighthouse using trigonometric principles. The problem involves a 25 feet high lighthouse, a distance of 80 feet from the foot of the hill, and an angle of 17°. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation