# Triangle calculator

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

Triangle has two solutions: a=3.4; b=3.19441125497; c=4.8 and a=3.4; b=3.59441125497; c=4.8.

### #1 Obtuse scalene triangle.

Sides: a = 3.4   b = 3.19441125497   c = 4.8

Area: T = 5.4210588745
Perimeter: p = 11.39441125497
Semiperimeter: s = 5.69770562748

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 41.62877133166° = 41°37'40″ = 0.72765406575 rad
Angle ∠ C = γ = 93.37222866834° = 93°22'20″ = 1.63296538327 rad

Height: ha = 3.18985816147
Height: hb = 3.39441125497
Height: hc = 2.25985786438

Median: ma = 3.70655603476
Median: mb = 3.84404962251
Median: mc = 2.26330018758

Inradius: r = 0.95114718626
Circumradius: R = 2.4044163056

Vertex coordinates: A[4.8; 0] B[0; 0] C[2.54114213562; 2.25985786438]
Centroid: CG[2.44771404521; 0.75328595479]
Coordinates of the circumscribed circle: U[2.4; -0.14114213562]
Coordinates of the inscribed circle: I[2.50329437252; 0.95114718626]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 138.3722286683° = 138°22'20″ = 0.72765406575 rad
∠ C' = γ' = 86.62877133166° = 86°37'40″ = 1.63296538327 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, c and angle α. ### 2. From angle α, side c and side a we calculate side b - 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 = 3.4   b = 3.59441125497   c = 4.8

Area: T = 6.0999411255
Perimeter: p = 11.79441125497
Semiperimeter: s = 5.89770562748

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 48.37222866834° = 48°22'20″ = 0.84442556693 rad
Angle ∠ C = γ = 86.62877133166° = 86°37'40″ = 1.51219388208 rad

Height: ha = 3.58878889735
Height: hb = 3.39441125497
Height: hc = 2.54114213562

Median: ma = 3.88444333576
Median: mb = 3.75110783443
Median: mc = 2.54553531209

Inradius: r = 1.03443145751
Circumradius: R = 2.4044163056

Vertex coordinates: A[4.8; 0] B[0; 0] C[2.25985786438; 2.54114213562]
Centroid: CG[2.35328595479; 0.84771404521]
Coordinates of the circumscribed circle: U[2.4; 0.14114213562]
Coordinates of the inscribed circle: I[2.30329437252; 1.03443145751]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 131.6287713317° = 131°37'40″ = 0.84442556693 rad
∠ C' = γ' = 93.37222866834° = 93°22'20″ = 1.51219388208 rad

# How did we calculate this triangle?

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