# 15 18 20 triangle

### Acute scalene triangle.

Sides: a = 15   b = 18   c = 20

Area: T = 129.7599151893
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 46.1287528069° = 46°7'39″ = 0.80550772406 rad
Angle ∠ B = β = 59.89896728258° = 59°53'23″ = 1.04552719788 rad
Angle ∠ C = γ = 73.98327991052° = 73°58'58″ = 1.29112434342 rad

Height: ha = 17.30112202524
Height: hb = 14.41876835437
Height: hc = 12.97659151893

Median: ma = 17.486570845
Median: mb = 15.21551240547
Median: mc = 13.21098448136

Inradius: r = 4.89765717695
Circumradius: R = 10.40438904409

Vertex coordinates: A[20; 0] B[0; 0] C[7.525; 12.97659151893]
Centroid: CG[9.175; 4.32553050631]
Coordinates of the circumscribed circle: U[10; 2.87107031031]
Coordinates of the inscribed circle: I[8.5; 4.89765717695]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.8722471931° = 133°52'21″ = 0.80550772406 rad
∠ B' = β' = 120.1110327174° = 120°6'37″ = 1.04552719788 rad
∠ C' = γ' = 106.0177200895° = 106°1'2″ = 1.29112434342 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    