Right Triangle Calculator
Provide any two sides of a right triangle — both legs, or one leg and the hypotenuse — and get the third side, both acute angles, the area, the perimeter and the altitude to the hypotenuse, all with working shown.
TheCalculators — Right Triangle Calculator
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Complete triangle
a = 3, b = 4, c = 5
α = 36.87° · β = 53.13° · area 6
- Leg a
- 3
- Leg b
- 4
- Hypotenuse c
- 5
- Angle α (opposite a)
- 36.8699°
- Angle β (opposite b)
- 53.1301°
- Angle γ (right angle)
- 90°
- Area A = ½ab
- 6
- Perimeter P = a+b+c
- 12
- Altitude to hypotenuse h = ab/c
- 2.4
Step-by-step solution
- 1Find the third side (Pythagoras)c = √(a² + b²) = √(3² + 4²) = 5
- 2Angle α via arcsinα = arcsin(a/c) = arcsin(0.6) = 36.8699°
- 3Angle β via arcsinβ = arcsin(b/c) = arcsin(0.8) = 53.1301° (check: α + β = 90°)
- 4Area and perimeterA = ½·a·b = ½·3·4 = 6 · P = 3 + 4 + 5 = 12
- 5Altitude to the hypotenuseh = a·b/c = 3·4/5 = 2.4
The two acute angles of a right triangle always sum to 90°, and the altitude h splits the triangle into two smaller similar triangles.
Most useful next
Formula
a² + b² = c² · α = arcsin(a/c) · β = arcsin(b/c) · A = ½ab · P = a+b+c · h = ab/c
Pro tips
- • Special triangles: 45-45-90 has sides a, a, a√2; 30-60-90 has sides 1, √3, 2 (scaled).
- • sin(α) = opposite/hypotenuse — with only sides known, arcsin gives the angle instantly.
- • Check yourself: α + β should always equal 90°.
FAQ
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