# 20 21 24 triangle

### Acute scalene triangle.

Sides: a = 20   b = 21   c = 24

Area: T = 199.2766033431
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 52.25882679659° = 52°15'30″ = 0.91220788374 rad
Angle ∠ B = β = 56.13112953983° = 56°7'53″ = 0.98796759181 rad
Angle ∠ C = γ = 71.61104366358° = 71°36'38″ = 1.25498378981 rad

Height: ha = 19.92876033431
Height: hb = 18.97986698506
Height: hc = 16.60663361193

Median: ma = 20.21113829314
Median: mb = 19.43657917256
Median: mc = 16.62882891483

Inradius: r = 6.13215702594
Circumradius: R = 12.64657755938

Vertex coordinates: A[24; 0] B[0; 0] C[11.14658333333; 16.60663361193]
Centroid: CG[11.71552777778; 5.53554453731]
Coordinates of the circumscribed circle: U[12; 3.989944111]
Coordinates of the inscribed circle: I[11.5; 6.13215702594]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.7421732034° = 127°44'30″ = 0.91220788374 rad
∠ B' = β' = 123.8698704602° = 123°52'7″ = 0.98796759181 rad
∠ C' = γ' = 108.3989563364° = 108°23'22″ = 1.25498378981 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.