Angles Of Elevation & Depression - Varsity Tutors

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Angles of Elevation & Depression

Study Guide

Key Definition

The $\text{angle of elevation}$ is the angle from the horizontal upward to an object. The $\text{angle of depression}$ is the angle from the horizontal downward to an object.

Important Notes

  • The angle of depression from one point and the corresponding angle of elevation from another point on a parallel horizontal line are congruent.
  • Remember to draw a horizontal line to help visualize the problem.
  • Trigonometry can often be used to solve these types of problems.

Mathematical Notation

$\angle$ denotes an angle.$\sin(\theta), \cos(\theta), \tan(\theta)$ denote trigonometric ratios.Remember to use proper notation when solving problems

Why It Works

These concepts work due to the properties of parallel lines and alternate interior angles.

Remember

Congruence of elevation and depression angles requires that the horizontal lines at both observation points be parallel.

Quick Reference

Angle of Elevation:Angle from the horizontal upward to an objectAngle of Depression:Angle from the horizontal downward to an object

Understanding Angles of Elevation & Depression

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Video explanation of this concept

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Beginner Explanation

Angles of elevation and depression are the angles formed when looking up or down respectively.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

If the angle of depression is 30 degrees, what is the angle of elevation?

A$30^\circ$B$60^\circ$C$45^\circ$D$90^\circ$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Observing a Bird

You are looking at a bird sitting on a tree. The angle of elevation to the bird is 45 degrees. If you move 20 feet further away from the tree, the angle of elevation to the bird becomes 30 degrees. Can you calculate how high the bird is from the ground?Show AnswerClick to reveal the detailed solution for this question exercise.3

Advanced Challenge

Thinking ExerciseAdvanced

Think About This

If the horizontal distance to an object of constant height h is halved, how does the tangent of the angle of elevation change?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.

Recap

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Review key concepts and takeaways

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