# Triangle calculator

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 = 1   b = 3.07876835372   c = 3.23660679775

Area: T = 1.53988417686
Perimeter: p = 7.31437515147
Semiperimeter: s = 3.65768757573

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

Height: ha = 3.07876835372
Height: hb = 1
Height: hc = 0.95110565163

Median: ma = 3.11880339887
Median: mb = 1.83552204197
Median: mc = 1.61880339887

Inradius: r = 0.42108077798
Circumradius: R = 1.61880339887

Vertex coordinates: A[3.23660679775; 0] B[0; 0] C[0.30990169944; 0.95110565163]
Centroid: CG[1.18216949906; 0.31770188388]
Coordinates of the circumscribed circle: U[1.61880339887; -0]
Coordinates of the inscribed circle: I[0.57991922202; 0.42108077798]

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 ### 10. Inradius ### 11. Circumradius ### 12. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.