30-60-90 Triangle Calculator

Your details

The short leg faces 30 deg, the long leg faces 60 deg, the hypotenuse faces the right angle, and the height is the altitude dropped from the right-angle vertex to the hypotenuse.
Enter the measurement of the value you selected above.
cm
Hypotenuse c (90 deg)
10cm
Short leg a (30 deg)5cm
Long leg b (60 deg)8.6603cm
Altitude h (to hypotenuse)4.3301cm
Area A21.6506cm²
Perimeter P23.6603cm
Inradius r1.8301cm
Circumradius R5cm

Sides: 5 / 8.66 / 10 cm | Area: 21.651 cm^2 | Altitude: 4.33 cm

  • The three sides hold the ratio 1 : √3 : 2. The long leg (8.66 cm) is √3 ≈ 1.732 times the short leg, and the hypotenuse (10 cm) is exactly twice the short leg.
  • The altitude from the right-angle vertex to the hypotenuse is 4.33 cm. This is also the geometric mean altitude, so h = a × b / c.
  • The circumradius (5 cm) equals the short leg and is exactly half the hypotenuse. The incircle has radius 1.83 cm.
  • Because the shape is determined entirely by its angles, a single measured value (side, height, area, or perimeter) is enough to reconstruct the whole triangle.

Next stepTo solve a right triangle without the 30-60-90 constraint, use the right triangle calculator.

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