# Triangle calculator

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

Triangle has two solutions: a=1.84767624318; b=6.2; c=7.5 and a=9.6443904215; b=6.2; c=7.5.

### #1 Obtuse scalene triangle.

Sides: a = 1.84767624318   b = 6.2   c = 7.5

Area: T = 4.45215350344
Perimeter: p = 15.54767624318
Semiperimeter: s = 7.77333812159

Angle ∠ A = α = 11.0388226456° = 11°2'18″ = 0.19326533952 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 128.9621773544° = 128°57'42″ = 2.25108075576 rad

Height: ha = 4.82109070726
Height: hb = 1.43659790434
Height: hc = 1.18770760092

Median: ma = 6.81985311564
Median: mb = 4.49766949796
Median: mc = 2.62196880997

Inradius: r = 0.57326639297
Circumradius: R = 4.82327438633

Vertex coordinates: A[7.5; 0] B[0; 0] C[1.41547020986; 1.18770760092]
Centroid: CG[2.97215673662; 0.39656920031]
Coordinates of the circumscribed circle: U[3.75; -3.03325498134]
Coordinates of the inscribed circle: I[1.57333812159; 0.57326639297]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.9621773544° = 168°57'42″ = 0.19326533952 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 51.0388226456° = 51°2'18″ = 2.25108075576 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 = 9.6443904215   b = 6.2   c = 7.5

Area: T = 23.2466183019
Perimeter: p = 23.3443904215
Semiperimeter: s = 11.67219521075

Angle ∠ A = α = 88.9621773544° = 88°57'42″ = 1.55326758568 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 51.0388226456° = 51°2'18″ = 0.8910785096 rad

Height: ha = 4.82109070726
Height: hb = 7.49987687158
Height: hc = 6.19989821384

Median: ma = 4.90985413183
Median: mb = 8.06333395224
Median: mc = 7.18774852524

Inradius: r = 1.99216276905
Circumradius: R = 4.82327438633

Vertex coordinates: A[7.5; 0] B[0; 0] C[7.38876592339; 6.19989821384]
Centroid: CG[4.9632553078; 2.06663273795]
Coordinates of the circumscribed circle: U[3.75; 3.03325498134]
Coordinates of the inscribed circle: I[5.47219521075; 1.99216276905]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 91.0388226456° = 91°2'18″ = 1.55326758568 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 128.9621773544° = 128°57'42″ = 0.8910785096 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    