# 12 21 24 triangle

### Acute scalene triangle.

Sides: a = 12   b = 21   c = 24

Area: T = 125.9879909112
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 29.99547255274° = 29°59'41″ = 0.52435067187 rad
Angle ∠ B = β = 61.02884677763° = 61°1'42″ = 1.06551477001 rad
Angle ∠ C = γ = 88.97768066963° = 88°58'37″ = 1.55329382348 rad

Height: ha = 20.99766515188
Height: hb = 11.99880865821
Height: hc = 10.49883257594

Median: ma = 21.73770651193
Median: mb = 15.80334806293
Median: mc = 12.1866057607

Inradius: r = 4.42203476882
Circumradius: R = 12.0021913723

Vertex coordinates: A[24; 0] B[0; 0] C[5.81325; 10.49883257594]
Centroid: CG[9.93875; 3.49994419198]
Coordinates of the circumscribed circle: U[12; 0.21443198879]
Coordinates of the inscribed circle: I[7.5; 4.42203476882]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0055274473° = 150°19″ = 0.52435067187 rad
∠ B' = β' = 118.9721532224° = 118°58'18″ = 1.06551477001 rad
∠ C' = γ' = 91.02331933037° = 91°1'23″ = 1.55329382348 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.