# Triangle calculator

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

Triangle has two solutions: a=50; b=60; c=14.14218130505 and a=50; b=60; c=77.78435201238.

### #1 Obtuse scalene triangle.

Sides: a = 50   b = 60   c = 14.14218130505

Area: T = 272.7055466221
Perimeter: p = 124.1421813051
Semiperimeter: s = 62.07109065252

Angle ∠ A = α = 40° = 0.69881317008 rad
Angle ∠ B = β = 129.5255165368° = 129°31'31″ = 2.26106405999 rad
Angle ∠ C = γ = 10.47548346316° = 10°28'29″ = 0.18328203529 rad

Height: ha = 10.90882186488
Height: hb = 9.09901822074
Height: hc = 38.56772565812

Median: ma = 35.70770782644
Median: mb = 21.21330959121
Median: mc = 54.77222765723

Inradius: r = 4.39334506758
Circumradius: R = 38.89330956715

Vertex coordinates: A[14.14218130505; 0] B[0; 0] C[-31.82108535366; 38.56772565812]
Centroid: CG[-5.89330134954; 12.85657521937]
Coordinates of the circumscribed circle: U[7.07109065252; 38.24549365515]
Coordinates of the inscribed circle: I[2.07109065252; 4.39334506758]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140° = 0.69881317008 rad
∠ B' = β' = 50.47548346316° = 50°28'29″ = 2.26106405999 rad
∠ C' = γ' = 169.5255165368° = 169°31'31″ = 0.18328203529 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   ### 10. Calculation of medians ### #2 Acute scalene triangle.

Sides: a = 50   b = 60   c = 77.78435201238

Area: T = 1499.94884892
Perimeter: p = 187.7843520124
Semiperimeter: s = 93.89217600619

Angle ∠ A = α = 40° = 0.69881317008 rad
Angle ∠ B = β = 50.47548346316° = 50°28'29″ = 0.88109520537 rad
Angle ∠ C = γ = 89.52551653684° = 89°31'31″ = 1.56325088991 rad

Height: ha = 59.9987939568
Height: hb = 49.99882829734
Height: hc = 38.56772565812

Median: ma = 64.80884716794
Median: mb = 58.09659379081
Median: mc = 39.21100879786

Inradius: r = 15.97552941921
Circumradius: R = 38.89330956715

Vertex coordinates: A[77.78435201238; 0] B[0; 0] C[31.82108535366; 38.56772565812]
Centroid: CG[36.53547912201; 12.85657521937]
Coordinates of the circumscribed circle: U[38.89217600619; 0.32223200297]
Coordinates of the inscribed circle: I[33.89217600619; 15.97552941921]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140° = 0.69881317008 rad
∠ B' = β' = 129.5255165368° = 129°31'31″ = 0.88109520537 rad
∠ C' = γ' = 90.47548346316° = 90°28'29″ = 1.56325088991 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    