# Triangle calculator - result

Please enter what you know about the triangle:
You have entered side a, median mc and angle β.

Triangle has two solutions: a=7; b=4.61096016282; c=6.36437138795 and a=7; b=10.71438515788; c=15.08655305278.

### #1 Acute scalene triangle.

Sides: a = 7   b = 4.61096016282   c = 6.36437138795

Area: T = 14.31768075168
Perimeter: p = 17.97333155077
Semiperimeter: s = 8.98766577539

Angle ∠ A = α = 77.45328590336° = 77°27'10″ = 1.35218074052 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 62.54771409664° = 62°32'50″ = 1.09216535476 rad

Height: ha = 4.09105164334
Height: hb = 6.21217331048
Height: hc = 4.54995132678

Median: ma = 4.3155395782
Median: mb = 6.28798344228
Median: mc = 5

Inradius: r = 1.59331181435
Circumradius: R = 3.58656335426

Vertex coordinates: A[6.36437138795; 0] B[0; 0] C[5.36223111018; 4.54995132678]
Centroid: CG[3.90986749938; 1.54998377559]
Coordinates of the circumscribed circle: U[3.18218569398; 1.65330439549]
Coordinates of the inscribed circle: I[4.37770561257; 1.59331181435]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.5477140966° = 102°32'50″ = 1.35218074052 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 117.4532859034° = 117°27'10″ = 1.09216535476 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle β and median mc. ### 2. From side a and angle β we calculate height hc: ### 3. From side a, angle β and median mc we calculate side c:  ### 4. Calculation of the third side b of the triangle using a Law of Cosines 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area using Heron's formula ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle using a Law of Cosines   ### 12. Calculation of medians ### #2 Obtuse scalene triangle.

Sides: a = 7   b = 10.71438515788   c = 15.08655305278

Area: T = 33.93987723808
Perimeter: p = 32.79993821066
Semiperimeter: s = 16.43996910533

Angle ∠ A = α = 24.8332793774° = 24°49'58″ = 0.43334140138 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 115.1677206226° = 115°10'2″ = 2.0110046939 rad

Height: ha = 9.69767921088
Height: hb = 6.3355494221
Height: hc = 4.54995132678

Median: ma = 12.60767411919
Median: mb = 10.46985224239
Median: mc = 5

Inradius: r = 2.06994763255
Circumradius: R = 8.33438970893

Vertex coordinates: A[15.08655305278; 0] B[0; 0] C[5.36223111018; 4.54995132678]
Centroid: CG[6.81659472099; 1.54998377559]
Coordinates of the circumscribed circle: U[7.54327652639; -3.54440842073]
Coordinates of the inscribed circle: I[5.68658394745; 2.06994763255]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1677206226° = 155°10'2″ = 0.43334140138 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 64.8332793774° = 64°49'58″ = 2.0110046939 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle β and median mc. ### 2. From side a and angle β we calculate height hc: ### 3. From side a, angle β and median mc we calculate side c:  ### 4. Calculation of the third side b of the triangle using a Law of Cosines 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area using Heron's formula ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle using a Law of Cosines    