# Triangle calculator

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

Triangle has two solutions: a=155; b=63; c=99.77106663709 and a=155; b=63; c=201.0211008775.

### #1 Obtuse scalene triangle.

Sides: a = 155   b = 63   c = 99.77106663709

Area: T = 1870.595492686
Perimeter: p = 317.7710666371
Semiperimeter: s = 158.8855333186

Angle ∠ A = α = 143.4732776509° = 143°28'22″ = 2.50440723371 rad
Angle ∠ B = β = 14° = 0.24443460953 rad
Angle ∠ C = γ = 22.52772234906° = 22°31'38″ = 0.39331742212 rad

Height: ha = 24.13767087337
Height: hb = 59.38439659321
Height: hc = 37.49878938179

Median: ma = 30.90986223253
Median: mb = 126.4810602995
Median: mc = 107.2777460508

Inradius: r = 11.77332385322
Circumradius: R = 130.2077313075

Vertex coordinates: A[99.77106663709; 0] B[0; 0] C[150.3965837573; 37.49878938179]
Centroid: CG[83.38988346479; 12.49992979393]
Coordinates of the circumscribed circle: U[49.88553331855; 120.2722182616]
Coordinates of the inscribed circle: I[95.88553331855; 11.77332385322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 36.52772234906° = 36°31'38″ = 2.50440723371 rad
∠ B' = β' = 166° = 0.24443460953 rad
∠ C' = γ' = 157.4732776509° = 157°28'22″ = 0.39331742212 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b 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   ### 10. Calculation of medians ### #2 Obtuse scalene triangle.

Sides: a = 155   b = 63   c = 201.0211008775

Area: T = 3768.93222211
Perimeter: p = 419.0211008775
Semiperimeter: s = 209.5110504387

Angle ∠ A = α = 36.52772234906° = 36°31'38″ = 0.63875203165 rad
Angle ∠ B = β = 14° = 0.24443460953 rad
Angle ∠ C = γ = 129.4732776509° = 129°28'22″ = 2.26597262418 rad

Height: ha = 48.63113834981
Height: hb = 119.649864194
Height: hc = 37.49878938179

Median: ma = 127.2122314594
Median: mb = 176.7065894028
Median: mc = 62.40770389284

Inradius: r = 17.98992279489
Circumradius: R = 130.2077313075

Vertex coordinates: A[201.0211008775; 0] B[0; 0] C[150.3965837573; 37.49878938179]
Centroid: CG[117.1398948782; 12.49992979393]
Coordinates of the circumscribed circle: U[100.5110504387; -82.77442887977]
Coordinates of the inscribed circle: I[146.5110504387; 17.98992279489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.4732776509° = 143°28'22″ = 0.63875203165 rad
∠ B' = β' = 166° = 0.24443460953 rad
∠ C' = γ' = 50.52772234906° = 50°31'38″ = 2.26597262418 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b 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    