# Triangle calculator

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

Triangle has two solutions: a=66.23224612987; b=121; c=164 and a=185.0330116044; b=121; c=164.

### #1 Obtuse scalene triangle.

Sides: a = 66.23224612987   b = 121   c = 164

Area: T = 3491.019924951
Perimeter: p = 351.2322461299
Semiperimeter: s = 175.6166230649

Angle ∠ A = α = 20.66002863319° = 20°36'1″ = 0.36595428233 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 119.4399713668° = 119°23'59″ = 2.08439181294 rad

Height: ha = 105.4177167989
Height: hb = 57.70327975126
Height: hc = 42.57334054818

Median: ma = 140.2566248587
Median: mb = 109.4588300119
Median: mc = 52.81992149207

Inradius: r = 19.87986822642
Circumradius: R = 94.12112915251

Vertex coordinates: A[164; 0] B[0; 0] C[50.7377008932; 42.57334054818]
Centroid: CG[71.57990029773; 14.19111351606]
Coordinates of the circumscribed circle: U[82; -46.20440855157]
Coordinates of the inscribed circle: I[54.61662306494; 19.87986822642]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.4399713668° = 159°23'59″ = 0.36595428233 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 60.66002863319° = 60°36'1″ = 2.08439181294 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 = 185.0330116044   b = 121   c = 164

Area: T = 9752.6755413
Perimeter: p = 470.0330116044
Semiperimeter: s = 235.0155058022

Angle ∠ A = α = 79.43997136681° = 79°23'59″ = 1.38657864286 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 60.66002863319° = 60°36'1″ = 1.05876745241 rad

Height: ha = 105.4177167989
Height: hb = 161.2011246496
Height: hc = 118.9355066012

Median: ma = 110.4966443559
Median: mb = 164.032994215
Median: mc = 133.0966100325

Inradius: r = 41.49880873782
Circumradius: R = 94.12112915251

Vertex coordinates: A[164; 0] B[0; 0] C[141.7411292205; 118.9355066012]
Centroid: CG[101.9143764069; 39.64550220041]
Coordinates of the circumscribed circle: U[82; 46.20440855157]
Coordinates of the inscribed circle: I[114.0155058022; 41.49880873782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.6600286332° = 100°36'1″ = 1.38657864286 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 119.4399713668° = 119°23'59″ = 1.05876745241 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    