Trig Word Problem Game

Trig Word Problem Quiz/Game
This game focuses on solving word problems involving trigonometry. SOH-CAH-TOA Focus: The problems are specifically designed to require identifying which side is the Opposite, Adjacent, or Hypotenuse (SOH-CAH-TOA). Includes a mix of finding missing lengths (like height of a building) and missing angles (like angle of elevation). Scroll down the page for a more detailed explanation.

 

 

How to Play the Trig Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Problem” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Trig Word Problems
Trigonometry word problems usually involve finding a missing side or angle in a right-angled triangle. Success comes down to mastering the SOH CAH TOA acronym and following a consistent workflow.

The Core Toolkit: SOH CAH TOA
Before starting, remember the three primary ratios:
SOH: \(\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}\)
CAH: \(\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}\)
TOA: \(\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}\)

The 5-Step Strategy
Step 1: Sketch the Scenario
Don’t try to solve it in your head. Draw a right triangle and label the parts:
Hypotenuse (H): The longest side, opposite the 90° angle.
Opposite (O): The side directly across from the given (or target) angle.
Adjacent (A): The side next to the angle that isn’t the hypotenuse.
Step 2: Identify Knowns and Unknowns
Write down what you have:
Angle (θ): e.g., 35°
Side 1: e.g., Adjacent = 10 m
Side 2 (Target): e.g., Opposite = x
Step 3: Choose Your Ratio
Look at Step 2. Which ratio uses the two sides you are dealing with?
If you have O and A, use Tangent.
If you have O and H, use Sine.
If you have A and H, use Cosine.
Step 4: Set Up the Equation
Plug your values into the formula.
Example: \(\tan(35^\circ) = \frac{x}{10}\)
Step 5: Solve
Finding a side: Isolate $x$ using algebra (x = 10 tan(35°).
Finding an angle: Use the inverse function on your calculator (\(\theta = \tan^{-1}(\frac{O}{A}))\).

Key Concepts to Remember
Angle of Elevation vs. Depression
Angle of Elevation: The angle looking up from a horizontal line.
Angle of Depression: The angle looking down from a horizontal line.
Crucial Tip: The angle of depression outside the triangle is equal to the angle of elevation inside the triangle (due to alternate interior angles).

Common Keywords
“Vertical height” or “Altitude”: Usually the Opposite side.
“Distance from base” or “Horizontal distance”: Usually the Adjacent side.
“Length of a ladder/string/wire”: Usually the Hypotenuse.

Worked Example
Problem: A 12 ft ladder leans against a building. The ladder makes a 70° angle with the ground. How high up the building does the ladder reach?
Sketch: The ladder is the Hypotenuse (12). The wall height is the Opposite side (x). The ground angle is 70°.
Knowns: θ = 70°, H = 12, O = x.
Ratio: Since we have O and H, use Sine (SOH).
Equation: \(\sin(70^\circ) = \frac{x}{12}\)
Solve: \(x = 12 \cdot \sin(70^\circ) \approx 11.28\text{ ft}\).
 

This video gives a clear, step-by-step approach to explain how to solve trig word problems.

• Show Video

 

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