# Triangle calculator

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

Triangle has two solutions: a=2.49329557658; b=20.2; c=18.3 and a=29.34326786799; b=20.2; c=18.3.

### #1 Obtuse scalene triangle.

Sides: a = 2.49329557658   b = 20.2   c = 18.3

Area: T = 15.50216499296
Perimeter: p = 40.99329557658
Semiperimeter: s = 20.49664778829

Angle ∠ A = α = 4.81110354856° = 4°48'40″ = 0.08439684097 rad
Angle ∠ B = β = 137.1898964514° = 137°11'20″ = 2.39443991282 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 12.43663618016
Height: hb = 1.53548168247
Height: hc = 1.69441693912

Median: ma = 19.23330780919
Median: mb = 8.27990346192
Median: mc = 11.10987764504

Inradius: r = 0.75663079871
Circumradius: R = 14.86220635962

Vertex coordinates: A[18.3; 0] B[0; 0] C[-1.82988298238; 1.69441693912]
Centroid: CG[5.49903900587; 0.56547231304]
Coordinates of the circumscribed circle: U[9.15; 11.71114659346]
Coordinates of the inscribed circle: I[0.29664778829; 0.75663079871]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.1898964514° = 175°11'20″ = 0.08439684097 rad
∠ B' = β' = 42.81110354856° = 42°48'40″ = 2.39443991282 rad
∠ C' = γ' = 142° = 0.66332251158 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle γ. ### 2. From angle γ, side b and side c we calculate side a - 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 = 29.34326786799   b = 20.2   c = 18.3

Area: T = 182.4588084145
Perimeter: p = 67.84326786799
Semiperimeter: s = 33.92113393399

Angle ∠ A = α = 99.18989645144° = 99°11'20″ = 1.73111740124 rad
Angle ∠ B = β = 42.81110354856° = 42°48'40″ = 0.74771935254 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 12.43663618016
Height: hb = 18.06551568461
Height: hc = 19.94107742235

Median: ma = 12.49986720084
Median: mb = 22.2769517194
Median: mc = 23.46989986164

Inradius: r = 5.37988584913
Circumradius: R = 14.86220635962

Vertex coordinates: A[18.3; 0] B[0; 0] C[21.52657593473; 19.94107742235]
Centroid: CG[13.27552531158; 6.64769247412]
Coordinates of the circumscribed circle: U[9.15; 11.71114659346]
Coordinates of the inscribed circle: I[13.72113393399; 5.37988584913]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 80.81110354856° = 80°48'40″ = 1.73111740124 rad
∠ B' = β' = 137.1898964514° = 137°11'20″ = 0.74771935254 rad
∠ C' = γ' = 142° = 0.66332251158 rad

# How did we calculate this triangle?

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