# 18 21 21 triangle

### Acute isosceles triangle.

Sides: a = 18   b = 21   c = 21

Area: T = 170.7632993649
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 50.75438670503° = 50°45'14″ = 0.88658220881 rad
Angle ∠ B = β = 64.62330664748° = 64°37'23″ = 1.12878852827 rad
Angle ∠ C = γ = 64.62330664748° = 64°37'23″ = 1.12878852827 rad

Height: ha = 18.9743665961
Height: hb = 16.26331422523
Height: hc = 16.26331422523

Median: ma = 18.9743665961
Median: mb = 16.5
Median: mc = 16.5

Inradius: r = 5.69220997883
Circumradius: R = 11.62113704011

Vertex coordinates: A[21; 0] B[0; 0] C[7.71442857143; 16.26331422523]
Centroid: CG[9.57114285714; 5.42110474174]
Coordinates of the circumscribed circle: U[10.5; 4.98105873148]
Coordinates of the inscribed circle: I[9; 5.69220997883]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.246613295° = 129°14'46″ = 0.88658220881 rad
∠ B' = β' = 115.3776933525° = 115°22'37″ = 1.12878852827 rad
∠ C' = γ' = 115.3776933525° = 115°22'37″ = 1.12878852827 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    