# 16 21 24 triangle

### Acute scalene triangle.

Sides: a = 16   b = 21   c = 24

Area: T = 165.2544160311
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 40.97880974811° = 40°58'41″ = 0.71552027222 rad
Angle ∠ B = β = 59.39551294361° = 59°23'42″ = 1.03766405683 rad
Angle ∠ C = γ = 79.62767730829° = 79°37'36″ = 1.3989749363 rad

Height: ha = 20.65767700388
Height: hb = 15.73884914582
Height: hc = 13.77111800259

Median: ma = 21.08331686423
Median: mb = 17.486570845
Median: mc = 14.33003496461

Inradius: r = 5.41881691905
Circumradius: R = 12.1999390298

Vertex coordinates: A[24; 0] B[0; 0] C[8.14658333333; 13.77111800259]
Centroid: CG[10.71552777778; 4.5990393342]
Coordinates of the circumscribed circle: U[12; 2.19766164078]
Coordinates of the inscribed circle: I[9.5; 5.41881691905]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0221902519° = 139°1'19″ = 0.71552027222 rad
∠ B' = β' = 120.6054870564° = 120°36'18″ = 1.03766405683 rad
∠ C' = γ' = 100.3733226917° = 100°22'24″ = 1.3989749363 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    