# 10 21 23 triangle

### Acute scalene triangle.

Sides: a = 10   b = 21   c = 23

Area: T = 104.9577134107
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 25.76601690897° = 25°45'37″ = 0.45495997665 rad
Angle ∠ B = β = 65.87770759881° = 65°52'37″ = 1.15497718776 rad
Angle ∠ C = γ = 88.36327549222° = 88°21'46″ = 1.54222210095 rad

Height: ha = 20.99114268214
Height: hb = 9.9965917534
Height: hc = 9.12767073137

Median: ma = 21.44876105895
Median: mb = 14.2921605928
Median: mc = 11.75879760163

Inradius: r = 3.88773012632
Circumradius: R = 11.50546967533

Vertex coordinates: A[23; 0] B[0; 0] C[4.08769565217; 9.12767073137]
Centroid: CG[9.02989855072; 3.04222357712]
Coordinates of the circumscribed circle: U[11.5; 0.32987056215]
Coordinates of the inscribed circle: I[6; 3.88773012632]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.243983091° = 154°14'23″ = 0.45495997665 rad
∠ B' = β' = 114.1232924012° = 114°7'23″ = 1.15497718776 rad
∠ C' = γ' = 91.63772450778° = 91°38'14″ = 1.54222210095 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.