Triangle calculator - result

Please enter what you know about the triangle:
You have entered side a and ratio of angles α:β:γ = 1:4:5.

Right scalene triangle.

Sides: a = 2   b = 6.15553670744   c = 6.4722135955

Area: T = 6.15553670744
Perimeter: p = 14.62875030294
Semiperimeter: s = 7.31437515147

Angle ∠ A = α = 18° = 0.31441592654 rad
Angle ∠ B = β = 72° = 1.25766370614 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 6.15553670744
Height: hb = 2
Height: hc = 1.90221130326

Median: ma = 6.23660679775
Median: mb = 3.67704408393
Median: mc = 3.23660679775

Inradius: r = 0.84216155597
Circumradius: R = 3.23660679775

Vertex coordinates: A[6.4722135955; 0] B[0; 0] C[0.61880339887; 1.90221130326]
Centroid: CG[2.36333899812; 0.63440376775]
Coordinates of the circumscribed circle: U[3.23660679775; -0]
Coordinates of the inscribed circle: I[1.15883844403; 0.84216155597]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162° = 0.31441592654 rad
∠ B' = β' = 108° = 1.25766370614 rad
∠ C' = γ' = 90° = 1.57107963268 rad

How did we calculate this triangle?

1. Input data entered: side a and ratio of angles α:β:γ. 2. From side a and angle β we calculate height hc: 3. From side a and angle γ we calculate height hb: 4. Calculation of the third side c 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area using Heron's formula 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle using a Law of Cosines     