# Triangle calculator

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

Triangle has two solutions: a=113.194354285; b=265; c=172 and a=359.043991497; b=265; c=172.

### #1 Obtuse scalene triangle.

Sides: a = 113.194354285   b = 265   c = 172

Area: T = 6809.015508386
Perimeter: p = 550.194354285
Semiperimeter: s = 275.0976771425

Angle ∠ A = α = 17.38438646978° = 17°23'2″ = 0.30334056757 rad
Angle ∠ B = β = 135.6166135302° = 135°36'58″ = 2.36769480799 rad
Angle ∠ C = γ = 27° = 0.4711238898 rad

Height: ha = 120.3077482431
Height: hb = 51.38987930858
Height: hc = 79.17545939984

Median: ma = 216.1054848313
Median: mb = 60.35501372945
Median: mc = 184.7243818365

Inradius: r = 24.75113449489
Circumradius: R = 189.4311276754

Vertex coordinates: A[172; 0] B[0; 0] C[-80.89659937705; 79.17545939984]
Centroid: CG[30.36880020765; 26.39215313328]
Coordinates of the circumscribed circle: U[86; 168.7854503473]
Coordinates of the inscribed circle: I[10.0976771425; 24.75113449489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6166135302° = 162°36'58″ = 0.30334056757 rad
∠ B' = β' = 44.38438646978° = 44°23'2″ = 2.36769480799 rad
∠ C' = γ' = 153° = 0.4711238898 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle γ. ### 2. From angle γ, side b and side c 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 = 359.043991497   b = 265   c = 172

Area: T = 21597.59441311
Perimeter: p = 796.043991497
Semiperimeter: s = 398.0219957485

Angle ∠ A = α = 108.6166135302° = 108°36'58″ = 1.89657091818 rad
Angle ∠ B = β = 44.38438646978° = 44°23'2″ = 0.77546445737 rad
Angle ∠ C = γ = 27° = 0.4711238898 rad

Height: ha = 120.3077482431
Height: hb = 163.0010710424
Height: hc = 251.1354815478

Median: ma = 132.9555198712
Median: mb = 248.3765885043
Median: mc = 303.5977315981

Inradius: r = 54.26325909203
Circumradius: R = 189.4311276754

Vertex coordinates: A[172; 0] B[0; 0] C[256.5954943435; 251.1354815478]
Centroid: CG[142.8654981145; 83.71216051594]
Coordinates of the circumscribed circle: U[86; 168.7854503473]
Coordinates of the inscribed circle: I[133.0219957485; 54.26325909203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 71.38438646978° = 71°23'2″ = 1.89657091818 rad
∠ B' = β' = 135.6166135302° = 135°36'58″ = 0.77546445737 rad
∠ C' = γ' = 153° = 0.4711238898 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle γ. ### 2. From angle γ, side b and side c 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    