Triangle calculator

Please enter what you know about the triangle:
You have entered side b, c and angle α.

Acute scalene triangle.

Sides: a = 22.58657330089   b = 31.57   c = 27.66

Area: T = 304.5010660219
Perimeter: p = 81.81657330089
Semiperimeter: s = 40.90878665044

Angle ∠ A = α = 44.22° = 44°13'12″ = 0.77217845952 rad
Angle ∠ B = β = 77.11993911128° = 77°7'10″ = 1.34659872921 rad
Angle ∠ C = γ = 58.66106088872° = 58°39'38″ = 1.02438207663 rad

Height: ha = 26.96439829798
Height: hb = 19.29105074576
Height: hc = 22.01774013173

Median: ma = 27.44770657104
Median: mb = 19.70986083419
Median: mc = 23.7099095676

Inradius: r = 7.44435722573
Circumradius: R = 16.19224557039

Vertex coordinates: A[27.66; 0] B[0; 0] C[5.03548162608; 22.01774013173]
Centroid: CG[10.89882720869; 7.33991337724]
Coordinates of the circumscribed circle: U[13.83; 8.42218003848]
Coordinates of the inscribed circle: I[9.33878665044; 7.44435722573]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.78° = 135°46'48″ = 0.77217845952 rad
∠ B' = β' = 102.8810608887° = 102°52'50″ = 1.34659872921 rad
∠ C' = γ' = 121.3399391113° = 121°20'22″ = 1.02438207663 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle α. 2. Calculation of the third side a of the triangle using a Law of Cosines Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 3. The triangle circumference is the sum of the lengths of its three sides 4. Semiperimeter of the triangle 5. The triangle area using Heron's formula 6. Calculate the heights of the triangle from its area. 7. Calculation of the inner angles of the triangle using a Law of Cosines     