# Triangle calculator

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

### Right scalene triangle.

Sides: a = 83   b = 101.3244290867   c = 58.11772256714

Area: T = 2411.865486536
Perimeter: p = 242.4421516539
Semiperimeter: s = 121.2210758269

Angle ∠ A = α = 55° = 0.96599310886 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 35° = 0.61108652382 rad

Height: ha = 58.11772256714
Height: hb = 47.60768442171
Height: hc = 83

Median: ma = 71.41333175237
Median: mb = 50.66221454336
Median: mc = 87.94397690464

Inradius: r = 19.89664674021
Circumradius: R = 50.66221454336

Vertex coordinates: A[58.11772256714; 0] B[0; 0] C[-0; 83]
Centroid: CG[19.37224085571; 27.66766666667]
Coordinates of the circumscribed circle: U[29.05986128357; 41.5]
Coordinates of the inscribed circle: I[19.89664674021; 19.89664674021]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125° = 0.96599310886 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 145° = 0.61108652382 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle α and angle β. ### 2. From angle α and angle β we calculate angle γ: ### 3. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b: ### 4. 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. ### 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.