# Triangle calculator

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

Triangle has two solutions: a=75.73114136849; b=124; c=164 and a=152.1176531826; b=124; c=164.

### #1 Obtuse scalene triangle.

Sides: a = 75.73114136849   b = 124   c = 164

Area: T = 4467.083283996
Perimeter: p = 363.7311413685
Semiperimeter: s = 181.8665706842

Angle ∠ A = α = 26.06109860088° = 26°3'40″ = 0.45548500122 rad
Angle ∠ B = β = 46° = 0.80328514559 rad
Angle ∠ C = γ = 107.9399013991° = 107°56'20″ = 1.88438911855 rad

Height: ha = 117.9721727255
Height: hb = 72.05497232251
Height: hc = 54.47766199995

Median: ma = 140.3644483561
Median: mb = 111.6766423247
Median: mc = 61.99001091223

Inradius: r = 24.56325352768
Circumradius: R = 86.1990142643

Vertex coordinates: A[164; 0] B[0; 0] C[52.60774604229; 54.47766199995]
Centroid: CG[72.20224868076; 18.15988733332]
Coordinates of the circumscribed circle: U[82; -26.54769525337]
Coordinates of the inscribed circle: I[57.86657068424; 24.56325352768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9399013991° = 153°56'20″ = 0.45548500122 rad
∠ B' = β' = 134° = 0.80328514559 rad
∠ C' = γ' = 72.06109860088° = 72°3'40″ = 1.88438911855 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle β. ### 2. From angle β, side c and side b 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 = 152.1176531826   b = 124   c = 164

Area: T = 8972.72550018
Perimeter: p = 440.1176531826
Semiperimeter: s = 220.0588265913

Angle ∠ A = α = 61.93990139912° = 61°56'20″ = 1.08110397296 rad
Angle ∠ B = β = 46° = 0.80328514559 rad
Angle ∠ C = γ = 72.06109860088° = 72°3'40″ = 1.25877014681 rad

Height: ha = 117.9721727255
Height: hb = 144.7211370997
Height: hc = 109.4233475632

Median: ma = 123.9899718266
Median: mb = 145.5121922629
Median: mc = 111.9544096072

Inradius: r = 40.77443147688
Circumradius: R = 86.1990142643

Vertex coordinates: A[164; 0] B[0; 0] C[105.6699022118; 109.4233475632]
Centroid: CG[89.89896740393; 36.47444918772]
Coordinates of the circumscribed circle: U[82; 26.54769525337]
Coordinates of the inscribed circle: I[96.05882659128; 40.77443147688]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.0610986009° = 118°3'40″ = 1.08110397296 rad
∠ B' = β' = 134° = 0.80328514559 rad
∠ C' = γ' = 107.9399013991° = 107°56'20″ = 1.25877014681 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle β. ### 2. From angle β, side c and side b 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    