# Triangle calculator

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

Triangle has two solutions: a=24.15; b=12.5; c=12.50220682648 and a=24.15; b=12.5; c=34.1522149145.

### #1 Obtuse scalene triangle.

Sides: a = 24.15   b = 12.5   c = 12.50220682648

Area: T = 39.0721963444
Perimeter: p = 49.15220682648
Semiperimeter: s = 24.57660341324

Angle ∠ A = α = 149.9977459766° = 149°59'51″ = 2.61879495425 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 15.00325402344° = 15°9″ = 0.26218437233 rad

Height: ha = 3.23657733701
Height: hb = 6.2521514151
Height: hc = 6.25504799392

Median: ma = 3.23657735472
Median: mb = 18.18551479359
Median: mc = 18.18440815626

Inradius: r = 1.59898400545
Circumradius: R = 24.14881456572

Vertex coordinates: A[12.50220682648; 0] B[0; 0] C[23.32771087049; 6.25504799392]
Centroid: CG[11.94330589899; 2.08334933131]
Coordinates of the circumscribed circle: U[6.25110341324; 23.32550404278]
Coordinates of the inscribed circle: I[12.07660341324; 1.59898400545]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.00325402344° = 30°9″ = 2.61879495425 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 164.9977459766° = 164°59'51″ = 0.26218437233 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b we calculate side c - 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 = 24.15   b = 12.5   c = 34.1522149145

Area: T = 106.7343661556
Perimeter: p = 70.8022149145
Semiperimeter: s = 35.40110745725

Angle ∠ A = α = 30.00325402344° = 30°9″ = 0.52436431111 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 134.9977459766° = 134°59'51″ = 2.35661501547 rad

Height: ha = 8.83992266299
Height: hb = 17.0777385849
Height: hc = 6.25504799392

Median: ma = 22.7054713621
Median: mb = 28.90990538692
Median: mc = 8.84399053838

Inradius: r = 3.01549836649
Circumradius: R = 24.14881456572

Vertex coordinates: A[34.1522149145; 0] B[0; 0] C[23.32771087049; 6.25504799392]
Centroid: CG[19.16597526166; 2.08334933131]
Coordinates of the circumscribed circle: U[17.07660745725; -17.07545604886]
Coordinates of the inscribed circle: I[22.90110745725; 3.01549836649]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.9977459766° = 149°59'51″ = 0.52436431111 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 45.00325402344° = 45°9″ = 2.35661501547 rad

# How did we calculate this triangle?

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