what is the angle of depression for a height of 417 feet and a distance of 819 feet

To find the angle of depression, we can use trigonometry. Specifically, the tangent function relates the angle of depression \(\theta\) to the opposite side (height) and the adjacent side (distance).

The formula is:

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

Given:
- Height (opposite side) = 417 feet
- Distance (adjacent side) = 819 feet

So,

\[
\tan(\theta) = \frac{417}{819}
\]

\[
\theta = \tan^{-1}\left(\frac{417}{819}\right)
\]

Let's calculate the angle \(\theta\).The angle of depression is approximately \(27^\circ\).

Would you like more details or have any questions? 

Here are 5 related questions:

1. How would the angle of depression change if the distance increased?
2. What is the angle of elevation for the same height and distance?
3. How can you calculate the horizontal distance if the angle of depression and height are known?
4. What trigonometric functions are involved in calculating angles of depression and elevation?
5. How does the angle of depression change with increasing height?

**Tip:** The angle of depression and the angle of elevation are always equal when measured from the horizontal.

Learn how to calculate the angle of depression using trigonometry with a height of 417 feet and a distance of 819 feet. Understand the relationship between the angle of depression, opposite side (height), and adjacent side (distance). Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation