# 70 67 82 triangle

### Acute scalene triangle.

Sides: a = 70   b = 67   c = 82

Area: T = 2248.363294612
Perimeter: p = 219
Semiperimeter: s = 109.5

Angle ∠ A = α = 54.93328655241° = 54°55'58″ = 0.9598759371 rad
Angle ∠ B = β = 51.57330979085° = 51°34'23″ = 0.9900120364 rad
Angle ∠ C = γ = 73.49440365675° = 73°29'39″ = 1.28327129187 rad

Height: ha = 64.23989413178
Height: hb = 67.11553118246
Height: hc = 54.83881206372

Median: ma = 66.19328999214
Median: mb = 68.48217493935
Median: mc = 54.89553549948

Inradius: r = 20.53329949418
Circumradius: R = 42.76222240287

Vertex coordinates: A[82; 0] B[0; 0] C[43.5066097561; 54.83881206372]
Centroid: CG[41.83553658537; 18.27993735457]
Coordinates of the circumscribed circle: U[41; 12.14993952065]
Coordinates of the inscribed circle: I[42.5; 20.53329949418]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.0677134476° = 125°4'2″ = 0.9598759371 rad
∠ B' = β' = 128.4276902092° = 128°25'37″ = 0.9900120364 rad
∠ C' = γ' = 106.5065963433° = 106°30'21″ = 1.28327129187 rad

# How did we calculate this triangle?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    