# 13 21 24 triangle

### Acute scalene triangle.

Sides: a = 13   b = 21   c = 24

Area: T = 136.2355090927
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 32.72655443586° = 32°43'32″ = 0.57111684986 rad
Angle ∠ B = β = 60.84546345737° = 60°50'41″ = 1.06219392055 rad
Angle ∠ C = γ = 86.43298210677° = 86°25'47″ = 1.50884849495 rad

Height: ha = 20.95992447581
Height: hb = 12.97547705645
Height: hc = 11.3532924244

Median: ma = 21.59328228817
Median: mb = 16.19441347407
Median: mc = 12.68985775404

Inradius: r = 4.69877617561
Circumradius: R = 12.02333339946

Vertex coordinates: A[24; 0] B[0; 0] C[6.33333333333; 11.3532924244]
Centroid: CG[10.11111111111; 3.78443080813]
Coordinates of the circumscribed circle: U[12; 0.74987057799]
Coordinates of the inscribed circle: I[8; 4.69877617561]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.2744455641° = 147°16'28″ = 0.57111684986 rad
∠ B' = β' = 119.1555365426° = 119°9'19″ = 1.06219392055 rad
∠ C' = γ' = 93.57701789323° = 93°34'13″ = 1.50884849495 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.