# Triangle calculator

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

### Right scalene triangle.

Sides: a = 36   b = 12.31327251597   c = 33.82989343483

Area: T = 208.2633185538
Perimeter: p = 82.1421659508
Semiperimeter: s = 41.0710829754

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 70° = 1.22217304764 rad

Height: ha = 11.57701769744
Height: hb = 33.82989343483
Height: hc = 12.31327251597

Median: ma = 18
Median: mb = 34.38545546628
Median: mc = 20.92113384047

Inradius: r = 5.0710829754
Circumradius: R = 18

Vertex coordinates: A[33.82989343483; 0] B[0; 0] C[33.82989343483; 12.31327251597]
Centroid: CG[22.55326228989; 4.10442417199]
Coordinates of the circumscribed circle: U[16.91444671741; 6.15663625799]
Coordinates of the inscribed circle: I[28.75881045943; 5.0710829754]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 110° = 1.22217304764 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle α, angle β and angle γ. ### 2. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b: ### 3. From angle γ, angle α and side a we calculate side c - By using the law of sines, we calculate unknown side c: 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. ### 4. The triangle circumference is the sum of the lengths of its three sides ### 5. Semiperimeter of the triangle ### 6. The triangle area using Heron's formula ### 7. Calculate the heights of the triangle from its area. ### 8. Calculation of the inner angles of the triangle using a Law of Cosines ### 9. Inradius ### 10. Circumradius ### 11. 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.