# 4 20 21 triangle

### Obtuse scalene triangle.

Sides: a = 4   b = 20   c = 21

Area: T = 39.50987015732
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 10.84440625637° = 10°50'39″ = 0.1899264596 rad
Angle ∠ B = β = 70.16766380911° = 70°10' = 1.22546388597 rad
Angle ∠ C = γ = 98.98992993452° = 98°59'21″ = 1.72876891978 rad

Height: ha = 19.75443507866
Height: hb = 3.95108701573
Height: hc = 3.76327334832

Median: ma = 20.4088331632
Median: mb = 11.33657840488
Median: mc = 9.88768599666

Inradius: r = 1.75659422921
Circumradius: R = 10.63105695524

Vertex coordinates: A[21; 0] B[0; 0] C[1.35771428571; 3.76327334832]
Centroid: CG[7.45223809524; 1.25442444944]
Coordinates of the circumscribed circle: U[10.5; -1.66110264926]
Coordinates of the inscribed circle: I[2.5; 1.75659422921]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.1565937436° = 169°9'21″ = 0.1899264596 rad
∠ B' = β' = 109.8333361909° = 109°50' = 1.22546388597 rad
∠ C' = γ' = 81.01107006548° = 81°39″ = 1.72876891978 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    