Triangle calculator

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

Triangle has two solutions: a=45; b=70.35218356535; c=99 and a=45; b=110.533016496; c=99.

#1 Obtuse scalene triangle.

Sides: a = 45   b = 70.35218356535   c = 99

Area: T = 1416.426613866
Perimeter: p = 214.3521835653
Semiperimeter: s = 107.1765917827

Angle ∠ A = α = 24° = 0.41988790205 rad
Angle ∠ B = β = 39.48553976237° = 39°29'7″ = 0.6899150195 rad
Angle ∠ C = γ = 116.5154602376° = 116°30'53″ = 2.03435634381 rad

Height: ha = 62.95222728294
Height: hb = 40.26769276645
Height: hc = 28.61546694679

Median: ma = 82.87990708798
Median: mb = 68.3798759897
Median: mc = 32.20215588117

Inradius: r = 13.21658993119
Circumradius: R = 55.31883500504

Vertex coordinates: A[99; 0] B[0; 0] C[34.7330400102; 28.61546694679]
Centroid: CG[44.5776800034; 9.5388223156]
Coordinates of the circumscribed circle: U[49.5; -24.69655431668]
Coordinates of the inscribed circle: I[36.82440821733; 13.21658993119]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156° = 0.41988790205 rad
∠ B' = β' = 140.5154602376° = 140°30'53″ = 0.6899150195 rad
∠ C' = γ' = 63.48553976237° = 63°29'7″ = 2.03435634381 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle α. 2. From angle α, side c and side a we calculate side b - 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 = 45   b = 110.533016496   c = 99

Area: T = 2225.355507859
Perimeter: p = 254.533016496
Semiperimeter: s = 127.265508248

Angle ∠ A = α = 24° = 0.41988790205 rad
Angle ∠ B = β = 92.51546023763° = 92°30'53″ = 1.61546844176 rad
Angle ∠ C = γ = 63.48553976237° = 63°29'7″ = 1.10880292155 rad

Height: ha = 98.90546701596
Height: hb = 40.26769276645
Height: hc = 44.95766682544

Median: ma = 102.4832723827
Median: mb = 53.46774729017
Median: mc = 68.34325832334

Inradius: r = 17.48659830774
Circumradius: R = 55.31883500504

Vertex coordinates: A[99; 0] B[0; 0] C[-1.97443301315; 44.95766682544]
Centroid: CG[32.34218899562; 14.98655560848]
Coordinates of the circumscribed circle: U[49.5; 24.69655431668]
Coordinates of the inscribed circle: I[16.73549175201; 17.48659830774]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156° = 0.41988790205 rad
∠ B' = β' = 87.48553976237° = 87°29'7″ = 1.61546844176 rad
∠ C' = γ' = 116.5154602376° = 116°30'53″ = 1.10880292155 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle α. 2. From angle α, side c and side a we calculate side b - 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     