# Triangle calculator

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

Triangle has two solutions: a=100.7321515488; b=123; c=165 and a=120.0821584611; b=123; c=165.

### #1 Obtuse scalene triangle.

Sides: a = 100.7321515488   b = 123   c = 165

Area: T = 6175.794362101
Perimeter: p = 388.7321515488
Semiperimeter: s = 194.3665757744

Angle ∠ A = α = 37.48985213058° = 37°29'19″ = 0.65442981285 rad
Angle ∠ B = β = 48° = 0.8387758041 rad
Angle ∠ C = γ = 94.51114786942° = 94°30'41″ = 1.65495364841 rad

Height: ha = 122.6198896204
Height: hb = 100.4199408472
Height: hc = 74.85881044971

Median: ma = 136.529944901
Median: mb = 122.0810584477
Median: mc = 76.36553658815

Inradius: r = 31.77440824963
Circumradius: R = 82.75664128708

Vertex coordinates: A[165; 0] B[0; 0] C[67.40325400376; 74.85881044971]
Centroid: CG[77.46875133459; 24.9532701499]
Coordinates of the circumscribed circle: U[82.5; -6.51095215831]
Coordinates of the inscribed circle: I[71.36657577438; 31.77440824963]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5111478694° = 142°30'41″ = 0.65442981285 rad
∠ B' = β' = 132° = 0.8387758041 rad
∠ C' = γ' = 85.48985213058° = 85°29'19″ = 1.65495364841 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 = 120.0821584611   b = 123   c = 165

Area: T = 7362.136567969
Perimeter: p = 408.0821584611
Semiperimeter: s = 204.0410792305

Angle ∠ A = α = 46.51114786942° = 46°30'41″ = 0.81217784432 rad
Angle ∠ B = β = 48° = 0.8387758041 rad
Angle ∠ C = γ = 85.48985213058° = 85°29'19″ = 1.49220561694 rad

Height: ha = 122.6198896204
Height: hb = 119.7109523247
Height: hc = 89.23880082387

Median: ma = 132.5659810121
Median: mb = 130.5387517524
Median: mc = 89.2643897973

Inradius: r = 36.08216854145
Circumradius: R = 82.75664128708

Vertex coordinates: A[165; 0] B[0; 0] C[80.35502635232; 89.23880082387]
Centroid: CG[81.78334211744; 29.74660027462]
Coordinates of the circumscribed circle: U[82.5; 6.51095215831]
Coordinates of the inscribed circle: I[81.04107923054; 36.08216854145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4898521306° = 133°29'19″ = 0.81217784432 rad
∠ B' = β' = 132° = 0.8387758041 rad
∠ C' = γ' = 94.51114786942° = 94°30'41″ = 1.49220561694 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    