# 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    