# 15 20 22 triangle

### Acute scalene triangle.

Sides: a = 15   b = 20   c = 22

Area: T = 145.7999305554
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 41.50879617794° = 41°30'29″ = 0.72444505988 rad
Angle ∠ B = β = 62.08436609946° = 62°5'1″ = 1.0843564296 rad
Angle ∠ C = γ = 76.40883772261° = 76°24'30″ = 1.33435777587 rad

Height: ha = 19.44399074072
Height: hb = 14.58799305554
Height: hc = 13.25444823231

Median: ma = 19.64105193414
Median: mb = 15.95330561335
Median: mc = 13.83883525031

Inradius: r = 5.11657651072
Circumradius: R = 11.31769263306

Vertex coordinates: A[22; 0] B[0; 0] C[7.02327272727; 13.25444823231]
Centroid: CG[9.67442424242; 4.41881607744]
Coordinates of the circumscribed circle: U[11; 2.65994776877]
Coordinates of the inscribed circle: I[8.5; 5.11657651072]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4922038221° = 138°29'31″ = 0.72444505988 rad
∠ B' = β' = 117.9166339005° = 117°54'59″ = 1.0843564296 rad
∠ C' = γ' = 103.5921622774° = 103°35'30″ = 1.33435777587 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    