# Triangle calculator

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

Triangle has two solutions: a=54; b=49; c=7.03329551737 and a=54; b=49; c=73.22766859779.

### #1 Obtuse scalene triangle.

Sides: a = 54   b = 49   c = 7.03329551737

Area: T = 127.0611070116
Perimeter: p = 110.0332955174
Semiperimeter: s = 55.01664775868

Angle ∠ A = α = 132.4898812327° = 132°29'20″ = 2.31223659972 rad
Angle ∠ B = β = 42° = 0.73330382858 rad
Angle ∠ C = γ = 5.51111876725° = 5°30'40″ = 0.09661883706 rad

Height: ha = 4.70659655599
Height: hb = 5.18661661272
Height: hc = 36.13330527434

Median: ma = 22.27662480961
Median: mb = 29.70765856207
Median: mc = 51.44105908343

Inradius: r = 2.31095093632
Circumradius: R = 36.61546754717

Vertex coordinates: A[7.03329551737; 0] B[0; 0] C[40.13298205758; 36.13330527434]
Centroid: CG[15.72109252498; 12.04443509145]
Coordinates of the circumscribed circle: U[3.51664775868; 36.44554228303]
Coordinates of the inscribed circle: I[6.01664775868; 2.31095093632]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 47.51111876725° = 47°30'40″ = 2.31223659972 rad
∠ B' = β' = 138° = 0.73330382858 rad
∠ C' = γ' = 174.4898812327° = 174°29'20″ = 0.09661883706 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 = 54   b = 49   c = 73.22766859779

Area: T = 1322.952185333
Perimeter: p = 176.2276685978
Semiperimeter: s = 88.11333429889

Angle ∠ A = α = 47.51111876725° = 47°30'40″ = 0.82992266564 rad
Angle ∠ B = β = 42° = 0.73330382858 rad
Angle ∠ C = γ = 90.48988123275° = 90°29'20″ = 1.57993277113 rad

Height: ha = 48.998821679
Height: hb = 53.99880348298
Height: hc = 36.13330527434

Median: ma = 56.14877850823
Median: mb = 59.48880136637
Median: mc = 36.30437617221

Inradius: r = 15.01442056635
Circumradius: R = 36.61546754717

Vertex coordinates: A[73.22766859779; 0] B[0; 0] C[40.13298205758; 36.13330527434]
Centroid: CG[37.78655021846; 12.04443509145]
Coordinates of the circumscribed circle: U[36.61333429889; -0.31223700869]
Coordinates of the inscribed circle: I[39.11333429889; 15.01442056635]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.4898812327° = 132°29'20″ = 0.82992266564 rad
∠ B' = β' = 138° = 0.73330382858 rad
∠ C' = γ' = 89.51111876725° = 89°30'40″ = 1.57993277113 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    