# 21 23 24 triangle

### Acute scalene triangle.

Sides: a = 21   b = 23   c = 24

Area: T = 220.4999433106
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 53.02662349852° = 53°1'34″ = 0.92554823904 rad
Angle ∠ B = β = 61.04547093922° = 61°2'41″ = 1.06554311698 rad
Angle ∠ C = γ = 65.92990556226° = 65°55'45″ = 1.15106790933 rad

Height: ha = 210.9999460101
Height: hb = 19.17438637483
Height: hc = 18.37549527588

Median: ma = 21.03297408448
Median: mb = 19.39771647413
Median: mc = 18.46661853126

Inradius: r = 6.48552774443
Circumradius: R = 13.14328909326

Vertex coordinates: A[24; 0] B[0; 0] C[10.16766666667; 18.37549527588]
Centroid: CG[11.38988888889; 6.12549842529]
Coordinates of the circumscribed circle: U[12; 5.36105579994]
Coordinates of the inscribed circle: I[11; 6.48552774443]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.9743765015° = 126°58'26″ = 0.92554823904 rad
∠ B' = β' = 118.9555290608° = 118°57'19″ = 1.06554311698 rad
∠ C' = γ' = 114.0710944377° = 114°4'15″ = 1.15106790933 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.