Triangle calculator - the result

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, area T, and angle β.

Obtuse scalene triangle.

Sides: a = 3   b = 16.26601938325   c = 18.93296126652

Area: T = 12
Perimeter: p = 38.19898064977
Semiperimeter: s = 19.09549032489

Angle ∠ A = α = 4.4722058555° = 4°28'19″ = 0.07880521461 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 150.5287941445° = 150°31'41″ = 2.62772081945 rad

Height: ha = 8
Height: hb = 1.47659971651
Height: hc = 1.26878547852

Median: ma = 17.58215832496
Median: mb = 10.8432815223
Median: mc = 6.86439924841

Inradius: r = 0.62884399477
Circumradius: R = 19.23774481944

Vertex coordinates: A[18.93296126652; 0] B[0; 0] C[2.71989233611; 1.26878547852]
Centroid: CG[7.21661786754; 0.42326182617]
Coordinates of the circumscribed circle: U[9.46548063326; -16.74880403068]
Coordinates of the inscribed circle: I[2.83547094164; 0.62884399477]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 175.5287941445° = 175°31'41″ = 0.07880521461 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 29.4722058555° = 29°28'19″ = 2.62772081945 rad

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How did we calculate this triangle?


1. Input data entered: side a, angle β, and area T.

a=3 β=25 T=12a = 3 \ \\ β = 25^\circ \ \\ T = 12

2. From side a and angle β we calculate height hc:

3. From area T and side a we calculate height ha - The area of the triangle is the product of the length of the base and the height divided by two:

4. From area T, side a and angle β we calculate side c:

5. From area T, side a and side c we calculate side b - using Heron's formula for the area and solve of the bikvadratic equation:


a=3 b=16.26 c=18.93

6. The triangle perimeter is the sum of the lengths of its three sides

7. Semiperimeter of the triangle


8. The triangle area using Heron's formula


9. Calculate the heights of the triangle from its area.


10. Calculation of the inner angles of the triangle using a Law of Cosines


a2=b2+c22bccosα  α=arccos(b2+c2a22bc)=arccos(16.262+18.932322 16.26 18.93)=42819"  b2=a2+c22accosβ β=arccos(a2+c2b22ac)=arccos(32+18.93216.2622 3 18.93)=25 γ=180αβ=18042819"25=1503141"

11. Inradius


12. Circumradius


R=abc4 rs=3 16.26 18.934 0.628 19.095=19.24

13. Calculation of medians


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