# Triangle calculator

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

Triangle has two solutions: a=3.92223491461; b=49; c=48 and a=24.73300779167; b=49; c=48.

### #1 Obtuse scalene triangle.

Sides: a = 3.92223491461   b = 49   c = 48

Area: T = 91.8998548003
Perimeter: p = 100.9222349146
Semiperimeter: s = 50.46111745731

Angle ∠ A = α = 4.48219495841° = 4°28'55″ = 0.07882247772 rad
Angle ∠ B = β = 102.5188050416° = 102°31'5″ = 1.78992775225 rad
Angle ∠ C = γ = 73° = 1.2744090354 rad

Height: ha = 46.85989330422
Height: hb = 3.7510961143
Height: hc = 3.82991061668

Median: ma = 48.46329115334
Median: mb = 23.65325349891
Median: mc = 25.14334367462

Inradius: r = 1.82111733829
Circumradius: R = 25.09766021557

Vertex coordinates: A[48; 0] B[0; 0] C[-0.85501580956; 3.82991061668]
Centroid: CG[15.71766139681; 1.27663687223]
Coordinates of the circumscribed circle: U[24; 7.3387536355]
Coordinates of the inscribed circle: I[1.46111745731; 1.82111733829]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5188050416° = 175°31'5″ = 0.07882247772 rad
∠ B' = β' = 77.48219495841° = 77°28'55″ = 1.78992775225 rad
∠ C' = γ' = 107° = 1.2744090354 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 Acute scalene triangle.

Sides: a = 24.73300779167   b = 49   c = 48

Area: T = 579.4132532614
Perimeter: p = 121.7330077917
Semiperimeter: s = 60.86550389584

Angle ∠ A = α = 29.51880504159° = 29°31'5″ = 0.51551871685 rad
Angle ∠ B = β = 77.48219495841° = 77°28'55″ = 1.35223151311 rad
Angle ∠ C = γ = 73° = 1.2744090354 rad

Height: ha = 46.85989330422
Height: hb = 23.64994911271
Height: hc = 24.14221888589

Median: ma = 46.98999553471
Median: mb = 29.28437561949
Median: mc = 30.50106291227

Inradius: r = 9.52196280579
Circumradius: R = 25.09766021557

Vertex coordinates: A[48; 0] B[0; 0] C[5.36601745184; 24.14221888589]
Centroid: CG[17.78767248395; 8.04773962863]
Coordinates of the circumscribed circle: U[24; 7.3387536355]
Coordinates of the inscribed circle: I[11.86550389584; 9.52196280579]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4821949584° = 150°28'55″ = 0.51551871685 rad
∠ B' = β' = 102.5188050416° = 102°31'5″ = 1.35223151311 rad
∠ C' = γ' = 107° = 1.2744090354 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    