# Triangle calculator

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

### Right scalene triangle.

Sides: a = 20.02110037192   b = 7.5   c = 18.56331514006

Area: T = 69.61218177523
Perimeter: p = 46.08441551198
Semiperimeter: s = 23.04220775599

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 22° = 0.38439724354 rad
Angle ∠ C = γ = 68° = 1.18768238914 rad

Height: ha = 6.95438789093
Height: hb = 18.56331514006
Height: hc = 7.5

Median: ma = 10.01105018596
Median: mb = 18.9388138502
Median: mc = 11.93330485409

Inradius: r = 3.02110738407
Circumradius: R = 10.01105018596

Vertex coordinates: A[18.56331514006; 0] B[0; 0] C[18.56331514006; 7.5]
Centroid: CG[12.37554342671; 2.5]
Coordinates of the circumscribed circle: U[9.28215757003; 3.75]
Coordinates of the inscribed circle: I[15.54220775599; 3.02110738407]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 158° = 0.38439724354 rad
∠ C' = γ' = 112° = 1.18768238914 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, angle α and angle β. ### 2. From angle α and angle β we calculate angle γ: ### 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: ### 4. Calculation of the third side c 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 ### 10. Inradius ### 11. Circumradius ### 12. 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.