# Triangle calculator - result

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

### Right scalene triangle.

Sides: a = 82.05550904813   b = 10   c = 81.44334642797

Area: T = 407.2177321399
Perimeter: p = 173.4998554761
Semiperimeter: s = 86.74992773805

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 7° = 0.12221730476 rad
Angle ∠ C = γ = 83° = 1.44986232792 rad

Height: ha = 9.92554615164
Height: hb = 81.44334642797
Height: hc = 10

Median: ma = 41.02875452406
Median: mb = 81.59768006351
Median: mc = 41.93216046494

Inradius: r = 4.69441868992
Circumradius: R = 41.02875452406

Vertex coordinates: A[81.44334642797; 0] B[0; 0] C[81.44334642797; 10]
Centroid: CG[54.29656428532; 3.33333333333]
Coordinates of the circumscribed circle: U[40.72217321399; 5]
Coordinates of the inscribed circle: I[76.74992773805; 4.69441868992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 173° = 0.12221730476 rad
∠ C' = γ' = 97° = 1.44986232792 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, angle α and angle β. ### 2. From angle α and angle β we calculate angle γ: ### 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: ### 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    