# 15 20 21 triangle

### Acute scalene triangle.

Sides: a = 15   b = 20   c = 21

Area: T = 142.7732546381
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ B = β = 65.02550346323° = 65°1'30″ = 1.13549009506 rad
Angle ∠ C = γ = 72.14215373016° = 72°8'30″ = 1.25991073534 rad

Height: ha = 19.03663395174
Height: hb = 14.27772546381
Height: hc = 13.59773853696

Median: ma = 19.0855334684
Median: mb = 15.26443375225
Median: mc = 14.22114626533

Inradius: r = 5.09990195136
Circumradius: R = 11.03215326015

Vertex coordinates: A[21; 0] B[0; 0] C[6.33333333333; 13.59773853696]
Centroid: CG[9.11111111111; 4.53224617899]
Coordinates of the circumscribed circle: U[10.5; 3.38330033311]
Coordinates of the inscribed circle: I[8; 5.09990195136]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ B' = β' = 114.9754965368° = 114°58'30″ = 1.13549009506 rad
∠ C' = γ' = 107.8588462698° = 107°51'30″ = 1.25991073534 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.