Real-World Examples of Sine, Cosine, and Tangent (SOH CAH TOA)

📚 Quick Study Guide

• 📐 SOH CAH TOA: This is a mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent:
  • SOH: Sine = Opposite / Hypotenuse
  • CAH: Cosine = Adjacent / Hypotenuse
  • TOA: Tangent = Opposite / Adjacent
• 🧭 Angle of Elevation: The angle from the horizontal upward to an object.
• 📉 Angle of Depression: The angle from the horizontal downward to an object.
• 📏 Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
• ➕ Adjacent: The side next to the angle (not the hypotenuse).
• ➖ Opposite: The side opposite the angle.

🧪 Practice Quiz

1. What trigonometric function would you use to find the height of a tree if you know the distance to the tree and the angle of elevation to the top?
   1. Sine
   2. Cosine
   3. Tangent
   4. Hypotenuse
2. A ladder leans against a wall, forming a 60-degree angle with the ground. If the foot of the ladder is 4 meters away from the wall, how long is the ladder? (Use cosine)
   1. 8 meters
   2. 6 meters
   3. 2 meters
   4. 4 meters
3. You're flying a kite, and you've let out 100 meters of string. The string makes an angle of 30 degrees with the ground. How high is the kite above the ground? (Use sine)
   1. 50 meters
   2. 86.6 meters
   3. 100 meters
   4. 200 meters
4. A surveyor needs to determine the height of a cliff. From a point 100 meters away from the base of the cliff, the angle of elevation to the top is 45 degrees. What is the height of the cliff? (Use tangent)
   1. 50 meters
   2. 100 meters
   3. 150 meters
   4. 200 meters
5. A ramp is 5 meters long and rises 1 meter vertically. What is the angle of elevation of the ramp?
   1. Approximately 11.5 degrees
   2. Approximately 20 degrees
   3. Approximately 30 degrees
   4. Approximately 45 degrees
6. A tower is supported by a wire that stretches from the top of the tower to the ground. The wire is 20 meters long and forms an angle of 60 degrees with the ground. How tall is the tower? (Use sine)
   1. 10 meters
   2. 17.32 meters
   3. 20 meters
   4. 40 meters
7. You are standing on top of a building that is 100 feet tall. You see a car moving towards the building. The angle of depression to the car changes from 45 degrees to 60 degrees. How far did the car travel?
   1. Approximately 26.79 feet
   2. Approximately 50 feet
   3. Approximately 73.21 feet
   4. Approximately 100 feet