Calculating and Applying Angles of Elevation and Depression

Understanding Angles of Elevation and Depression

Angles of elevation and depression are used to describe the angle between the horizontal line of sight and the line of sight up to or down to an object.

• Angle of Elevation: The angle formed when looking up at an object above the horizontal line.
• Angle of Depression: The angle formed when looking down at an object below the horizontal line.

These angles are often used in real-life applications such as navigation, construction, and physics.

Calculating Angles of Elevation and Depression

To calculate these angles, we use trigonometric ratios such as sine, cosine, and tangent.

• Tangent Ratio: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ This is commonly used for calculating angles of elevation and depression.

Steps to Calculate Angles

1. Identify the Right Triangle: Determine the right triangle formed by the horizontal line, the line of sight, and the vertical line.
2. Measure or Find the Lengths: Measure or find the lengths of the opposite and adjacent sides of the angle.
3. Use the Tangent Ratio: Use the tangent ratio to find the angle $\theta$.
4. Calculate the Angle: Use a calculator to find the angle using the inverse tangent function $\tan^{-1}$.

 

Worked Example

 

Applications of Angles of Elevation and Depression

These angles are used in various fields such as:

• Architecture: Designing buildings and structures.
• Aviation: Pilots use these angles for navigation.
• Surveying: Measuring land and planning construction projects.