# 8 15 21 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 15   c = 21

Area: T = 46.4332747065
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 17.14662099989° = 17°8'46″ = 0.29992578187 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 129.2966480239° = 129°17'47″ = 2.25766492914 rad

Height: ha = 11.60881867662
Height: hb = 6.1911032942
Height: hc = 4.42221663871

Median: ma = 17.80444938148
Median: mb = 14.00989257261
Median: mc = 5.85223499554

Inradius: r = 2.1110579412
Circumradius: R = 13.5688010506

Vertex coordinates: A[21; 0] B[0; 0] C[6.66766666667; 4.42221663871]
Centroid: CG[9.22222222222; 1.47440554624]
Coordinates of the circumscribed circle: U[10.5; -8.59330733205]
Coordinates of the inscribed circle: I[7; 2.1110579412]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.8543790001° = 162°51'14″ = 0.29992578187 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 50.70435197608° = 50°42'13″ = 2.25766492914 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    