Angles of Elevation & Depression Worksheet/Game

Angles of Elevation & Depression Worksheet/Game
Welcome to Angles of Elevation & Depression Worksheet/Game. In this game, you’ll need to apply your knowledge of Angles of Elevation and Depression to find the heights of objects or the distances between objects. Scroll down the page for a more detailed explanation.

 

 

1. The Core Objective
   Your goal is to solve 10 survey cases using right-angled trigonometry. For each case, you’ll be given a scenario (like a lighthouse or a ladder) and must calculate a missing value—usually the height of an object or the horizontal distance from it.
   

2. Understanding the Concepts
   To pick the right answer, you need to visualize the triangle:
   
   Angle of Elevation: This is the angle formed when looking up from the ground to an object.
   
   Angle of Depression: This is the angle formed when looking down from a height.
   
   The angle of depression is always equal to the angle of elevation from the ground. You can treat them the same when setting up your triangle
   

3. The Math Strategy (SOH-CAH-TOA)
   Most problems in this game use the Tangent function because you are usually dealing with the Opposite (height) and Adjacent (horizontal distance).
   \(\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}\)
   
   To find Height: Multiply the distance by the tangent of the angle:
   Height = Distance · tan(θ).
   
   To find Distance: Divide the height by the tangent:
   \(\text{Distance} = \frac{\text{Height}}{\tan(\theta)}\).
   
   Watch for Ladders: If the problem mentions a ladder leaning, you might need Sine or Cosine because the ladder itself is the Hypotenuse.
   

4. Game Controls
   The Options: Click one of the four buttons to submit your answer.
   Feedback:
   Gold (Correct): You’ve acquired the target! Your accuracy percentage will increase.
   Red (Wrong): The correct answer will be highlighted for you.
   Show Steps: If you get a question wrong, a “Show Steps” button will appear. Click it to see the exact formula and calculation used to solve that specific case.
   Navigation: Use the Next Case button to move forward or Return to Base to restart the game.
   

5. Tips
   Round to the nearest whole: All answers are rounded, so pick the choice closest to your calculation.
   Isosceles Alert: If the angle is 45°, the height and the distance are exactly the same.
   The “Shadow” is the Base: When a problem mentions a shadow, that is always your “Adjacent” side on the ground.
   

Angles of Elevation & Depression

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