# Triangle calculator

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

Triangle has two solutions: a=522.0288097964; b=3623.57; c=4000 and a=5497.29111732; b=3623.57; c=4000.

### #1 Obtuse scalene triangle.

Sides: a = 522.0288097964   b = 3623.57   c = 4000

Area: T = 687708.8122029
Perimeter: p = 8145.598809796
Semiperimeter: s = 4072.799904898

Angle ∠ A = α = 5.44552086439° = 5°26'43″ = 0.09550368193 rad
Angle ∠ B = β = 41.2° = 41°12' = 0.71990756518 rad
Angle ∠ C = γ = 133.3554791356° = 133°21'17″ = 2.32774801825 rad

Height: ha = 2634.758784047
Height: hb = 379.5755287371
Height: hc = 343.8544406015

Median: ma = 3807.493280218
Median: mb = 2203.110957088
Median: mc = 1643.589949862

Inradius: r = 168.8544098559
Circumradius: R = 2750.591054334

Vertex coordinates: A[4000; 0] B[0; 0] C[392.782172377; 343.8544406015]
Centroid: CG[1464.261057459; 114.6188135338]
Coordinates of the circumscribed circle: U[2000; -1888.319891827]
Coordinates of the inscribed circle: I[449.2299048982; 168.8544098559]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.5554791356° = 174°33'17″ = 0.09550368193 rad
∠ B' = β' = 138.8° = 138°48' = 0.71990756518 rad
∠ C' = γ' = 46.64552086439° = 46°38'43″ = 2.32774801825 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 Obtuse scalene triangle.

Sides: a = 5497.29111732   b = 3623.57   c = 4000

Area: T = 7242015.510998
Perimeter: p = 13120.86111732
Semiperimeter: s = 6560.43105866

Angle ∠ A = α = 92.15547913561° = 92°9'17″ = 1.60884045307 rad
Angle ∠ B = β = 41.2° = 41°12' = 0.71990756518 rad
Angle ∠ C = γ = 46.64552086439° = 46°38'43″ = 0.81441124711 rad

Height: ha = 2634.758784047
Height: hb = 3997.17215794
Height: hc = 3621.008775499

Median: ma = 2647.655504016
Median: mb = 4452.813262072
Median: mc = 4204.193253769

Inradius: r = 1103.893332139
Circumradius: R = 2750.591054334

Vertex coordinates: A[4000; 0] B[0; 0] C[4136.244383726; 3621.008775499]
Centroid: CG[2712.081127909; 1207.0032585]
Coordinates of the circumscribed circle: U[2000; 1888.319891827]
Coordinates of the inscribed circle: I[2936.86105866; 1103.893332139]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 87.84552086439° = 87°50'43″ = 1.60884045307 rad
∠ B' = β' = 138.8° = 138°48' = 0.71990756518 rad
∠ C' = γ' = 133.3554791356° = 133°21'17″ = 0.81441124711 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    