Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Practical Applications

Measuring Heights and Distances

Trigonometry in the Real World

Want to know how tall a tree is without climbing it? Trigonometry is the answer! By measuring an angle from a certain distance, you can calculate heights using tangent.

  • Stand a known distance from the object.
  • Measure the angle to the top.
  • Use \( \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \) to find the height.

This is how surveyors, architects, and even astronauts measure things they can't touch!

Examples

  • To find the height of a building, stand 30 meters away and measure an angle of elevation of 45°. Using tangent, the building is also 30 meters tall.

  • A drone flying at a known height can determine its distance from a landing pad by measuring the angle of depression.