# Triangle calculator

You have entered side a, b and angle β.

Triangle has two solutions: a=39.7; b=26.8; c=17.54551037532 and a=39.7; b=26.8; c=48.89439827355.

### #1 Obtuse scalene triangle.

Sides: a = 39.7   b = 26.8   c = 17.54551037532

Area: T = 190.7700013317
Perimeter: p = 84.04551037532
Semiperimeter: s = 42.02325518766

Angle ∠ A = α = 125.7943604984° = 125°47'37″ = 2.19655125849 rad
Angle ∠ B = β = 33.2° = 33°12' = 0.57994493117 rad
Angle ∠ C = γ = 21.00663950164° = 21°23″ = 0.3676630757 rad

Height: ha = 9.60770535676
Height: hb = 14.23113442774
Height: hc = 21.73882599727

Median: ma = 10.90993002917
Median: mb = 27.61215977961
Median: mc = 32.71440235002

Vertex coordinates: A[17.54551037532; 0] B[0; 0] C[33.22195432443; 21.73882599727]
Centroid: CG[16.92215489992; 7.24660866576]
Coordinates of the circumscribed circle: U[8.77325518766; 22.84656571132]
Coordinates of the inscribed circle: I[15.22325518766; 4.53880398096]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 54.20663950164° = 54°12'23″ = 2.19655125849 rad
∠ B' = β' = 146.8° = 146°48' = 0.57994493117 rad
∠ C' = γ' = 158.9943604984° = 158°59'37″ = 0.3676630757 rad

# How did we calculate this triangle?

### 2. From angle β, side a and b we calculate 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.

### #2 Obtuse scalene triangle.

Sides: a = 39.7   b = 26.8   c = 48.89439827355

Area: T = 531.4355053901
Perimeter: p = 115.3943982736
Semiperimeter: s = 57.69769913677

Angle ∠ A = α = 54.20663950164° = 54°12'23″ = 0.94660800687 rad
Angle ∠ B = β = 33.2° = 33°12' = 0.57994493117 rad
Angle ∠ C = γ = 92.59436049836° = 92°35'37″ = 1.61660632733 rad

Height: ha = 26.7732546796
Height: hb = 39.65993323807
Height: hc = 21.73882599727

Median: ma = 34.06547658713
Median: mb = 42.47111169369
Median: mc = 23.4421621383

Vertex coordinates: A[48.89439827355; 0] B[0; 0] C[33.22195432443; 21.73882599727]
Centroid: CG[27.37111753266; 7.24660866576]
Coordinates of the circumscribed circle: U[24.44769913677; -1.10773971405]
Coordinates of the inscribed circle: I[30.89769913677; 9.21107931679]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.7943604984° = 125°47'37″ = 0.94660800687 rad
∠ B' = β' = 146.8° = 146°48' = 0.57994493117 rad
∠ C' = γ' = 87.40663950164° = 87°24'23″ = 1.61660632733 rad

# How did we calculate this triangle?

### 2. From angle β, side a and b we calculate 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.