# 10 23 24 triangle

### Acute scalene triangle.

Sides: a = 10   b = 23   c = 24

Area: T = 114.2344134566
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 24.45495467105° = 24°26'58″ = 0.42767250907 rad
Angle ∠ B = β = 72.16766172902° = 72°10' = 1.26595450817 rad
Angle ∠ C = γ = 83.38438359994° = 83°23'2″ = 1.45553224811 rad

Height: ha = 22.84768269132
Height: hb = 9.93334030057
Height: hc = 9.52195112138

Median: ma = 22.96773681557
Median: mb = 14.34439882878
Median: mc = 13.05875648572

Inradius: r = 4.00882152479
Circumradius: R = 12.08804521805

Vertex coordinates: A[24; 0] B[0; 0] C[3.06325; 9.52195112138]
Centroid: CG[9.02108333333; 3.17331704046]
Coordinates of the circumscribed circle: U[12; 1.3921878186]
Coordinates of the inscribed circle: I[5.5; 4.00882152479]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.555045329° = 155°33'2″ = 0.42767250907 rad
∠ B' = β' = 107.833338271° = 107°50' = 1.26595450817 rad
∠ C' = γ' = 96.61661640006° = 96°36'58″ = 1.45553224811 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.