# 11 20 22 triangle

### Acute scalene triangle.

Sides: a = 11   b = 20   c = 22

Area: T = 109.6110389562
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 29.88329034608° = 29°52'58″ = 0.52215550554 rad
Angle ∠ B = β = 64.94108471732° = 64°56'27″ = 1.13334316022 rad
Angle ∠ C = γ = 85.1766249366° = 85°10'34″ = 1.48766059959 rad

Height: ha = 19.92991617386
Height: hb = 10.96110389562
Height: hc = 9.96545808693

Median: ma = 20.29216238877
Median: mb = 14.23302494708
Median: mc = 11.8111011811

Inradius: r = 4.13662411156
Circumradius: R = 11.03990995309

Vertex coordinates: A[22; 0] B[0; 0] C[4.65990909091; 9.96545808693]
Centroid: CG[8.88663636364; 3.32215269564]
Coordinates of the circumscribed circle: U[11; 0.92882879151]
Coordinates of the inscribed circle: I[6.5; 4.13662411156]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.1177096539° = 150°7'2″ = 0.52215550554 rad
∠ B' = β' = 115.0599152827° = 115°3'33″ = 1.13334316022 rad
∠ C' = γ' = 94.8243750634° = 94°49'25″ = 1.48766059959 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    