# Triangle calculator

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

Triangle has two solutions: a=800; b=250; c=560.0187787443 and a=800; b=250; c=1031.217724515.

### #1 Obtuse scalene triangle.

Sides: a = 800   b = 250   c = 560.0187787443

Area: T = 23415.11994896
Perimeter: p = 1610.018778744
Semiperimeter: s = 805.0098893722

Angle ∠ A = α = 160.4588406089° = 160°27'30″ = 2.80105274988 rad
Angle ∠ B = β = 6° = 0.10547197551 rad
Angle ∠ C = γ = 13.54215939107° = 13°32'30″ = 0.23663453997 rad

Height: ha = 58.5387798724
Height: hb = 187.3210955917
Height: hc = 83.62327706141

Median: ma = 167.5111077623
Median: mb = 679.1066001392
Median: mc = 522.3465689593

Inradius: r = 29.08767836023
Circumradius: R = 1195.847652919

Vertex coordinates: A[560.0187787443; 0] B[0; 0] C[795.6187516295; 83.62327706141]
Centroid: CG[451.8788434579; 27.87442568714]
Coordinates of the circumscribed circle: U[280.0098893722; 1162.602222811]
Coordinates of the inscribed circle: I[555.0098893722; 29.08767836023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 19.54215939107° = 19°32'30″ = 2.80105274988 rad
∠ B' = β' = 174° = 0.10547197551 rad
∠ C' = γ' = 166.4588406089° = 166°27'30″ = 0.23663453997 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 = 800   b = 250   c = 1031.217724515

Area: T = 43116.62215721
Perimeter: p = 2081.217724515
Semiperimeter: s = 1040.609862257

Angle ∠ A = α = 19.54215939107° = 19°32'30″ = 0.34110651548 rad
Angle ∠ B = β = 6° = 0.10547197551 rad
Angle ∠ C = γ = 154.4588406089° = 154°27'30″ = 2.69658077436 rad

Height: ha = 107.792155393
Height: hb = 344.9332972577
Height: hc = 83.62327706141

Median: ma = 634.7876974774
Median: mb = 914.3743831287
Median: mc = 292.2298931368

Inradius: r = 41.43440421911
Circumradius: R = 1195.847652919

Vertex coordinates: A[1031.217724515; 0] B[0; 0] C[795.6187516295; 83.62327706141]
Centroid: CG[608.945492048; 27.87442568714]
Coordinates of the circumscribed circle: U[515.6098622573; -1078.97994575]
Coordinates of the inscribed circle: I[790.6098622573; 41.43440421911]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.4588406089° = 160°27'30″ = 0.34110651548 rad
∠ B' = β' = 174° = 0.10547197551 rad
∠ C' = γ' = 25.54215939107° = 25°32'30″ = 2.69658077436 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    