# Triangle calculator

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

### Acute scalene triangle.

Sides: a = 9.7   b = 11.8   c = 12.2044005321

Area: T = 53.1999103519
Perimeter: p = 33.7044005321
Semiperimeter: s = 16.85220026605

Angle ∠ A = α = 47.63326246401° = 47°37'57″ = 0.83113461313 rad
Angle ∠ B = β = 64° = 1.11770107213 rad
Angle ∠ C = γ = 68.36773753599° = 68°22'3″ = 1.1933235801 rad

Height: ha = 10.96988873235
Height: hb = 9.01767972066
Height: hc = 8.71883022491

Median: ma = 10.98802719883
Median: mb = 9.31114914454
Median: mc = 8.91223825957

Inradius: r = 3.15768416283
Circumradius: R = 6.56443514488

Vertex coordinates: A[12.2044005321; 0] B[0; 0] C[4.25222001239; 8.71883022491]
Centroid: CG[5.4855401815; 2.90661007497]
Coordinates of the circumscribed circle: U[6.10220026605; 2.42199738583]
Coordinates of the inscribed circle: I[5.05220026605; 3.15768416283]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.367737536° = 132°22'3″ = 0.83113461313 rad
∠ B' = β' = 116° = 1.11770107213 rad
∠ C' = γ' = 111.633262464° = 111°37'57″ = 1.1933235801 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b we calculate side c - 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.