# 15 21 21 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 21   c = 21

Area: T = 147.1132839345
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 41.85496648553° = 41°50'59″ = 0.73304144426 rad
Angle ∠ B = β = 69.07551675724° = 69°4'31″ = 1.20655891055 rad
Angle ∠ C = γ = 69.07551675724° = 69°4'31″ = 1.20655891055 rad

Height: ha = 19.61550452459
Height: hb = 14.01107466042
Height: hc = 14.01107466042

Median: ma = 19.61550452459
Median: mb = 14.92548115566
Median: mc = 14.92548115566

Inradius: r = 5.16218540121
Circumradius: R = 11.24113709597

Vertex coordinates: A[21; 0] B[0; 0] C[5.35771428571; 14.01107466042]
Centroid: CG[8.78657142857; 4.67702488681]
Coordinates of the circumscribed circle: U[10.5; 4.01547753427]
Coordinates of the inscribed circle: I[7.5; 5.16218540121]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.1550335145° = 138°9'1″ = 0.73304144426 rad
∠ B' = β' = 110.9254832428° = 110°55'29″ = 1.20655891055 rad
∠ C' = γ' = 110.9254832428° = 110°55'29″ = 1.20655891055 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.