# Triangle calculator

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

Triangle has two solutions: a=120; b=32.92325682786; c=141 and a=120; b=166.4821544016; c=141.

### #1 Obtuse scalene triangle.

Sides: a = 120   b = 32.92325682786   c = 141

Area: T = 1641.224387552
Perimeter: p = 293.9232568279
Semiperimeter: s = 146.9611284139

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 11.18662009828° = 11°11'10″ = 0.19552360379 rad
Angle ∠ C = γ = 123.8143799017° = 123°48'50″ = 2.16109584523 rad

Height: ha = 27.35437312586
Height: hb = 99.70220561473
Height: hc = 23.28797712839

Median: ma = 82.96105192307
Median: mb = 129.8832739902
Median: mc = 52.64769158739

Inradius: r = 11.16877295495
Circumradius: R = 84.85328137424

Vertex coordinates: A[141; 0] B[0; 0] C[117.7220228716; 23.28797712839]
Centroid: CG[86.24400762387; 7.76599237613]
Coordinates of the circumscribed circle: U[70.5; -47.22202287161]
Coordinates of the inscribed circle: I[114.0398715861; 11.16877295495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 168.8143799017° = 168°48'50″ = 0.19552360379 rad
∠ C' = γ' = 56.18662009828° = 56°11'10″ = 2.16109584523 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, c and angle α. ### 2. From angle α, side c and side a we calculate side b - 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 ### 8. Inradius ### 9. Circumradius ### 10. Calculation of medians ### #2 Acute scalene triangle.

Sides: a = 120   b = 166.4821544016   c = 141

Area: T = 8299.276612448
Perimeter: p = 427.4821544016
Semiperimeter: s = 213.7410772008

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 78.81437990172° = 78°48'50″ = 1.37655602889 rad
Angle ∠ C = γ = 56.18662009828° = 56°11'10″ = 0.98106342013 rad

Height: ha = 138.3211268741
Height: hb = 99.70220561473
Height: hc = 117.7220228716

Median: ma = 142.1221610774
Median: mb = 101.0521837566
Median: mc = 126.8387700424

Inradius: r = 38.8298699113
Circumradius: R = 84.85328137424

Vertex coordinates: A[141; 0] B[0; 0] C[23.28797712839; 117.7220228716]
Centroid: CG[54.76599237613; 39.24400762387]
Coordinates of the circumscribed circle: U[70.5; 47.22202287161]
Coordinates of the inscribed circle: I[47.2599227992; 38.8298699113]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 101.1866200983° = 101°11'10″ = 1.37655602889 rad
∠ C' = γ' = 123.8143799017° = 123°48'50″ = 0.98106342013 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, c and angle α. ### 2. From angle α, side c and side a we calculate side b - 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 ### 8. Inradius ### 9. Circumradius ### 10. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.