# Triangle calculator

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

Triangle has two solutions: a=7.9099114914; b=33; c=38 and a=44.88549212409; b=33; c=38.

### #1 Obtuse scalene triangle.

Sides: a = 7.9099114914   b = 33   c = 38

Area: T = 108.0977481719
Perimeter: p = 78.9099114914
Semiperimeter: s = 39.4554557457

Angle ∠ A = α = 9.92876383247° = 9°55'40″ = 0.17332699757 rad
Angle ∠ B = β = 46° = 0.80328514559 rad
Angle ∠ C = γ = 124.0722361675° = 124°4'20″ = 2.1655471222 rad

Height: ha = 27.33549124129
Height: hb = 6.55113625284
Height: hc = 5.68993411431

Median: ma = 35.36875200618
Median: mb = 21.93223288632
Median: mc = 14.6555273773

Inradius: r = 2.74397970903
Circumradius: R = 22.93876992518

Vertex coordinates: A[38; 0] B[0; 0] C[5.49441328779; 5.68993411431]
Centroid: CG[14.49880442926; 1.89664470477]
Coordinates of the circumscribed circle: U[19; -12.8510604926]
Coordinates of the inscribed circle: I[6.4554557457; 2.74397970903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.0722361675° = 170°4'20″ = 0.17332699757 rad
∠ B' = β' = 134° = 0.80328514559 rad
∠ C' = γ' = 55.92876383247° = 55°55'40″ = 2.1655471222 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 = 44.88549212409   b = 33   c = 38

Area: T = 613.4632695389
Perimeter: p = 115.8854921241
Semiperimeter: s = 57.94224606204

Angle ∠ A = α = 78.07223616753° = 78°4'20″ = 1.3632619766 rad
Angle ∠ B = β = 46° = 0.80328514559 rad
Angle ∠ C = γ = 55.92876383247° = 55°55'40″ = 0.97661214316 rad

Height: ha = 27.33549124129
Height: hb = 37.18795572963
Height: hc = 32.28875102836

Median: ma = 27.61994851744
Median: mb = 38.17216920951
Median: mc = 34.50883769163

Inradius: r = 10.58774463877
Circumradius: R = 22.93876992518

Vertex coordinates: A[38; 0] B[0; 0] C[31.18796862474; 32.28875102836]
Centroid: CG[23.06598954158; 10.76325034279]
Coordinates of the circumscribed circle: U[19; 12.8510604926]
Coordinates of the inscribed circle: I[24.94224606204; 10.58774463877]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.9287638325° = 101°55'40″ = 1.3632619766 rad
∠ B' = β' = 134° = 0.80328514559 rad
∠ C' = γ' = 124.0722361675° = 124°4'20″ = 0.97661214316 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    