Triangle calculator

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

Triangle has two solutions: a=35; b=54; c=21.78221496582 and a=35; b=54; c=77.63223745147.

#1 Obtuse scalene triangle.

Sides: a = 35   b = 54   c = 21.78221496582

Area: T = 229.7966025756
Perimeter: p = 110.7822149658
Semiperimeter: s = 55.39110748291

Angle ∠ A = α = 23° = 0.4011425728 rad
Angle ∠ B = β = 142.9266264341° = 142°55'35″ = 2.49545339003 rad
Angle ∠ C = γ = 14.0743735659° = 14°4'25″ = 0.24656330253 rad

Height: ha = 13.13112014717
Height: hb = 8.51109639169
Height: hc = 21.09994809384

Median: ma = 37.26990356981
Median: mb = 10.9887766919
Median: mc = 44.18801368158

Inradius: r = 4.14986110617
Circumradius: R = 44.78878316418

Vertex coordinates: A[21.78221496582; 0] B[0; 0] C[-27.92551124282; 21.09994809384]
Centroid: CG[-2.04876542567; 7.03331603128]
Coordinates of the circumscribed circle: U[10.89110748291; 43.44334615592]
Coordinates of the inscribed circle: I[1.39110748291; 4.14986110617]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157° = 0.4011425728 rad
∠ B' = β' = 37.0743735659° = 37°4'25″ = 2.49545339003 rad
∠ C' = γ' = 165.9266264341° = 165°55'35″ = 0.24656330253 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 Obtuse scalene triangle.

Sides: a = 35   b = 54   c = 77.63223745147

Area: T = 819.0011403138
Perimeter: p = 166.6322374515
Semiperimeter: s = 83.31661872573

Angle ∠ A = α = 23° = 0.4011425728 rad
Angle ∠ B = β = 37.0743735659° = 37°4'25″ = 0.64770587533 rad
Angle ∠ C = γ = 119.9266264341° = 119°55'35″ = 2.09331081724 rad

Height: ha = 46.88000801793
Height: hb = 30.33333853014
Height: hc = 21.09994809384

Median: ma = 64.53879174315
Median: mb = 53.82327905853
Median: mc = 23.74545489914

Inradius: r = 9.83300393969
Circumradius: R = 44.78878316418

Vertex coordinates: A[77.63223745147; 0] B[0; 0] C[27.92551124282; 21.09994809384]
Centroid: CG[35.1865828981; 7.03331603128]
Coordinates of the circumscribed circle: U[38.81661872573; -22.34439806208]
Coordinates of the inscribed circle: I[29.31661872573; 9.83300393969]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157° = 0.4011425728 rad
∠ B' = β' = 142.9266264341° = 142°55'35″ = 0.64770587533 rad
∠ C' = γ' = 60.0743735659° = 60°4'25″ = 2.09331081724 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     