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Right Triangle Calculator

Solve a right triangle. Enter any two sides — the third, angles, area, and perimeter are calculated automatically.

abc90°BA

Right triangle formulas

SOHsin θ = oppositehypotenuse
CAHcos θ = adjacenthypotenuse
TOAtan θ = oppositeadjacent
Pythagorasa2 + b2 = c2
AreaArea = ½ab
AnglesA + B = 90°

Worked examples

  1. The hypotenuse is 10 and one angle is 30°. Find the legs and area.

    1. opposite = 10 × sin 30° = 5
    2. adjacent = 10 × cos 30° ≈ 8.660
    3. Area = ½ × 5 × 8.660

    Answer: Legs 5 and ≈ 8.66, Area ≈ 21.65

  2. The legs are 6 and 8. Find the hypotenuse and angles.

    1. c = √36 + 64 = 10
    2. A = tan−1(6/8) ≈ 36.87°
    3. B = 90° − 36.87° = 53.13°

    Answer: c = 10, angles ≈ 36.87° and 53.13°, Area = 24

Tips & common mistakes

  • Make sure your calculator is in degree mode, not radians.