Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 60.34333651663   b = 60.34333651663   c = 111.5

Area: T = 1287.40216402
Perimeter: p = 232.1876730333
Semiperimeter: s = 116.0933365166

Angle ∠ A = α = 22.5° = 22°30' = 0.39326990817 rad
Angle ∠ B = β = 22.5° = 22°30' = 0.39326990817 rad
Angle ∠ C = γ = 135° = 2.35661944902 rad

Height: ha = 42.66992027087
Height: hb = 42.66992027087
Height: hc = 23.09224061023

Median: ma = 84.41883358631
Median: mb = 84.41883358631
Median: mc = 23.09224061023

Inradius: r = 11.08993644814
Circumradius: R = 78.84224061023

Vertex coordinates: A[111.5; 0] B[0; 0] C[55.75; 23.09224061023]
Centroid: CG[55.75; 7.69774687008]
Coordinates of the circumscribed circle: U[55.75; -55.75]
Coordinates of the inscribed circle: I[55.75; 11.08993644814]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.5° = 157°30' = 0.39326990817 rad
∠ B' = β' = 157.5° = 157°30' = 0.39326990817 rad
∠ C' = γ' = 45° = 2.35661944902 rad

How did we calculate this triangle?

1. Input data entered: side c, angle α, angle β and angle γ. 2. From angle α, angle γ and side c we calculate side a - By using the law of sines, we calculate unknown side a: 3. Calculation of the third side b 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. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     