# 13 22 30 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 22   c = 30

Area: T = 128.9880376414
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 23.00773759133° = 23°27″ = 0.40215544619 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 115.5833001977° = 115°34'59″ = 2.01773039438 rad

Height: ha = 19.8433134833
Height: hb = 11.72554887649
Height: hc = 8.5998691761

Median: ma = 25.49901941931
Median: mb = 20.33546994077
Median: mc = 10.07547208398

Inradius: r = 3.96986269666
Circumradius: R = 16.63304368124

Vertex coordinates: A[30; 0] B[0; 0] C[9.75; 8.5998691761]
Centroid: CG[13.25; 2.8666230587]
Coordinates of the circumscribed circle: U[15; -7.18113249872]
Coordinates of the inscribed circle: I[10.5; 3.96986269666]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9932624087° = 156°59'33″ = 0.40215544619 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 64.41769980226° = 64°25'1″ = 2.01773039438 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    