# 15 20 23 triangle

### Acute scalene triangle.

Sides: a = 15   b = 20   c = 23

Area: T = 148.0687552151
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 40.07436640149° = 40°4'25″ = 0.69994173804 rad
Angle ∠ B = β = 59.13332322064° = 59°8' = 1.03220695993 rad
Angle ∠ C = γ = 80.79331037787° = 80°47'35″ = 1.41101056738 rad

Height: ha = 19.74223402868
Height: hb = 14.80767552151
Height: hc = 12.87554393175

Median: ma = 20.20551973512
Median: mb = 16.64333169771
Median: mc = 13.42657215821

Inradius: r = 5.10657776604
Circumradius: R = 11.65500879156

Vertex coordinates: A[23; 0] B[0; 0] C[7.69656521739; 12.87554393175]
Centroid: CG[10.2321884058; 4.29218131058]
Coordinates of the circumscribed circle: U[11.5; 1.86440140665]
Coordinates of the inscribed circle: I[9; 5.10657776604]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9266335985° = 139°55'35″ = 0.69994173804 rad
∠ B' = β' = 120.8676767794° = 120°52' = 1.03220695993 rad
∠ C' = γ' = 99.20768962213° = 99°12'25″ = 1.41101056738 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.