# 7 8 13 triangle

### Obtuse scalene triangle.

Sides: a = 7   b = 8   c = 13

Area: T = 24.2498711306
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 27.7965772496° = 27°47'45″ = 0.48551277482 rad
Angle ∠ B = β = 32.2044227504° = 32°12'15″ = 0.5622069803 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 6.92882032303
Height: hb = 6.06221778265
Height: hc = 3.73105709701

Median: ma = 10.21102889283
Median: mb = 9.6443650761
Median: mc = 3.77549172176

Inradius: r = 1.73220508076
Circumradius: R = 7.50655534995

Vertex coordinates: A[13; 0] B[0; 0] C[5.92330769231; 3.73105709701]
Centroid: CG[6.30876923077; 1.24435236567]
Coordinates of the circumscribed circle: U[6.5; -3.75327767497]
Coordinates of the inscribed circle: I[6; 1.73220508076]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.2044227504° = 152°12'15″ = 0.48551277482 rad
∠ B' = β' = 147.7965772496° = 147°47'45″ = 0.5622069803 rad
∠ C' = γ' = 60° = 2.09443951024 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    