🔺 Solving Right Triangles

Right triangle trigonometry forms the foundation for all trigonometric applications. This systematic approach ensures accurate solutions to any right triangle problem.

Step-by-Step Method

  1. Identify Known Elements: Label all given sides/angles on the triangle diagram
  2. Determine Missing Components: Note which sides/angles need calculation
  3. Select Appropriate Tools: Choose from:
    • Pythagorean Theorem (a² + b² = c²)
    • SOH-CAH-TOA ratios
    • Complementary angles (sum to 90°)

Practical Example

Given right triangle ABC with:
∠C = 90°
Side a = 5
Side b = 12
Find hypotenuse c and angles A, B

Solution:
1. c = √(5² + 12²) = 13 (Pythagorean Theorem)
2. tanA = 5/12 ⇒ A ≈ 22.62°
3. B = 90° - 22.62° ≈ 67.38°

Special Right Triangles

TypeAnglesSide Ratios
45-45-9045°, 45°, 90°1 : 1 : √2
30-60-9030°, 60°, 90°1 : √3 : 2

Memory Aid: For 30-60-90 triangles, think "1, 2, √3" with 2 always opposite the 90° angle.

Applications

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