# 15 20 30 triangle

### Obtuse scalene triangle.

Sides: a = 15   b = 20   c = 30

Area: T = 133.3177056298
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 36.33660575146° = 36°20'10″ = 0.63441838408 rad
Angle ∠ C = γ = 117.2879612736° = 117°16'47″ = 2.04769153877 rad

Height: ha = 17.77656075064
Height: hb = 13.33217056298
Height: hc = 8.88878037532

Median: ma = 24.3676985862
Median: mb = 21.50658131676
Median: mc = 9.35441434669

Inradius: r = 4.10220632707
Circumradius: R = 16.87770603138

Vertex coordinates: A[30; 0] B[0; 0] C[12.08333333333; 8.88878037532]
Centroid: CG[14.02877777778; 2.96326012511]
Coordinates of the circumscribed circle: U[15; -7.73553193105]
Coordinates of the inscribed circle: I[12.5; 4.10220632707]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 143.6643942485° = 143°39'50″ = 0.63441838408 rad
∠ C' = γ' = 62.7220387264° = 62°43'13″ = 2.04769153877 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    