# Triangle calculator - result

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

### Right scalene triangle.

Sides: a = 100   b = 40   c = 91.65215138991

Area: T = 1833.033027798
Perimeter: p = 231.6521513899
Semiperimeter: s = 115.826575695

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 23.57881784782° = 23°34'41″ = 0.41215168461 rad
Angle ∠ C = γ = 66.42218215218° = 66°25'19″ = 1.15992794807 rad

Height: ha = 36.66106055596
Height: hb = 91.65215138991
Height: hc = 40

Median: ma = 50
Median: mb = 93.80883151965
Median: mc = 60.8287625303

Inradius: r = 15.82657569496
Circumradius: R = 50

Vertex coordinates: A[91.65215138991; 0] B[0; 0] C[91.65215138991; 40]
Centroid: CG[61.10110092661; 13.33333333333]
Coordinates of the circumscribed circle: U[45.82657569496; 20]
Coordinates of the inscribed circle: I[75.82657569496; 15.82657569496]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 156.4221821522° = 156°25'19″ = 0.41215168461 rad
∠ C' = γ' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic equation:  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    