# 13 23 24 triangle

### Acute scalene triangle.

Sides: a = 13   b = 23   c = 24

Area: T = 146.3565731012
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 32.02439959746° = 32°1'26″ = 0.55989241694 rad
Angle ∠ B = β = 69.74877532578° = 69°44'52″ = 1.21773279402 rad
Angle ∠ C = γ = 78.22882507676° = 78°13'42″ = 1.3655340544 rad

Height: ha = 22.51662663095
Height: hb = 12.72765853054
Height: hc = 12.19663109177

Median: ma = 22.58987139962
Median: mb = 15.5
Median: mc = 14.31878210633

Inradius: r = 4.87985243671
Circumradius: R = 12.25878049223

Vertex coordinates: A[24; 0] B[0; 0] C[4.5; 12.19663109177]
Centroid: CG[9.5; 4.06554369726]
Coordinates of the circumscribed circle: U[12; 2.50107561882]
Coordinates of the inscribed circle: I[7; 4.87985243671]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.9766004025° = 147°58'34″ = 0.55989241694 rad
∠ B' = β' = 110.2522246742° = 110°15'8″ = 1.21773279402 rad
∠ C' = γ' = 101.7721749232° = 101°46'18″ = 1.3655340544 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.