# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 30.95552980808   b = 72.13436967816   c = 60

Area: T = 914.5510526403
Perimeter: p = 163.0898994862
Semiperimeter: s = 81.54444974312

Angle ∠ A = α = 25° = 0.4366332313 rad
Angle ∠ B = β = 100° = 1.7455329252 rad
Angle ∠ C = γ = 55° = 0.96599310886 rad

Height: ha = 59.08884651807
Height: hb = 25.35770957044
Height: hc = 30.48550175468

Median: ma = 64.51441650017
Median: mb = 31.27877506671
Median: mc = 46.6998504744

Inradius: r = 11.21553554834
Circumradius: R = 36.62332376628

Vertex coordinates: A[60; 0] B[0; 0] C[-5.37553311009; 30.48550175468]
Centroid: CG[18.20882229664; 10.16216725156]
Coordinates of the circumscribed circle: U[30; 21.00662261463]
Coordinates of the inscribed circle: I[9.41108006496; 11.21553554834]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155° = 0.4366332313 rad
∠ B' = β' = 80° = 1.7455329252 rad
∠ C' = γ' = 125° = 0.96599310886 rad

# How did we calculate this triangle?

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