# 15 18 21 triangle

### Acute scalene triangle.

Sides: a = 15   b = 18   c = 21

Area: T = 132.272244611
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ B = β = 57.12216504356° = 57°7'18″ = 0.99769608743 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 17.6366326148
Height: hb = 14.69769384567
Height: hc = 12.597737582

Median: ma = 18.06223918682
Median: mb = 15.87545078664
Median: mc = 12.8166005618

Inradius: r = 4.89989794856
Circumradius: R = 10.71765176247

Vertex coordinates: A[21; 0] B[0; 0] C[8.14328571429; 12.597737582]
Centroid: CG[9.71442857143; 4.19991252733]
Coordinates of the circumscribed circle: U[10.5; 2.14333035249]
Coordinates of the inscribed circle: I[9; 4.89989794856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ B' = β' = 122.8788349564° = 122°52'42″ = 0.99769608743 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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.