# 8 30 30 triangle

### Acute isosceles triangle.

Sides: a = 8   b = 30   c = 30

Area: T = 118.9298549979
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 15.32545113215° = 15°19'28″ = 0.26774631788 rad
Angle ∠ B = β = 82.33877443392° = 82°20'16″ = 1.43770647374 rad
Angle ∠ C = γ = 82.33877443392° = 82°20'16″ = 1.43770647374 rad

Height: ha = 29.73221374946
Height: hb = 7.92985699986
Height: hc = 7.92985699986

Median: ma = 29.73221374946
Median: mb = 16.03112195419
Median: mc = 16.03112195419

Inradius: r = 3.49878985288
Circumradius: R = 15.13551378649

Vertex coordinates: A[30; 0] B[0; 0] C[1.06766666667; 7.92985699986]
Centroid: CG[10.35655555556; 2.64328566662]
Coordinates of the circumscribed circle: U[15; 2.0188018382]
Coordinates of the inscribed circle: I[4; 3.49878985288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6755488678° = 164°40'32″ = 0.26774631788 rad
∠ B' = β' = 97.66222556608° = 97°39'44″ = 1.43770647374 rad
∠ C' = γ' = 97.66222556608° = 97°39'44″ = 1.43770647374 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    