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Study guides › Level 9 · Trigonometry

Heights and distances with angles

Level 9 · Trigonometry · for questions like “A kite string is 80 feet long at 30° to the ground. How high is the kite?”

💡 The idea

Measuring things you can't climb: make a right triangle and use sin, cos or tan with the angle you know.

A kite string at 30 degrees

✏️ Worked examples

1. Kite string 80 feet at 30°: height = 80 × sin 30° = 80 × 1/2 = 40 feet.

2. Standing 25 m from a tree, looking up 45°: height = 25 × tan 45° = 25 m.

3. A 20-foot ladder at 60° to the ground: distance from the wall = 20 × cos 60° = 10 feet.

⚠️ Watch out

🎯 Try these

  1. Kite string 50 feet at 30°: height?
  2. 60 m from a building, looking up 45°: height?
  3. A 36-foot ladder at 60°: distance from the wall?

Answers: 1) 25 feet 2) 60 m 3) 18 feet

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