# 21 29 29 triangle

### Acute isosceles triangle.

Sides: a = 21   b = 29   c = 29

Area: T = 283.8440073809
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 42.45546255238° = 42°27'17″ = 0.74109729981 rad
Angle ∠ B = β = 68.77326872381° = 68°46'22″ = 1.22003098277 rad
Angle ∠ C = γ = 68.77326872381° = 68°46'22″ = 1.22003098277 rad

Height: ha = 27.03223879818
Height: hb = 19.57551775041
Height: hc = 19.57551775041

Median: ma = 27.03223879818
Median: mb = 20.75545175805
Median: mc = 20.75545175805

Inradius: r = 7.18658246534
Circumradius: R = 15.55554145007

Vertex coordinates: A[29; 0] B[0; 0] C[7.60334482759; 19.57551775041]
Centroid: CG[12.20111494253; 6.5255059168]
Coordinates of the circumscribed circle: U[14.5; 5.63221328364]
Coordinates of the inscribed circle: I[10.5; 7.18658246534]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.5455374476° = 137°32'43″ = 0.74109729981 rad
∠ B' = β' = 111.2277312762° = 111°13'38″ = 1.22003098277 rad
∠ C' = γ' = 111.2277312762° = 111°13'38″ = 1.22003098277 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    