# 8 21 24 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 21   c = 24

Area: T = 82.10332124828
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 19.01444375634° = 19°52″ = 0.33218645409 rad
Angle ∠ B = β = 58.78664577123° = 58°47'11″ = 1.02660172427 rad
Angle ∠ C = γ = 102.1999104724° = 102°11'57″ = 1.784371087 rad

Height: ha = 20.52658031207
Height: hb = 7.81993535698
Height: hc = 6.84219343736

Median: ma = 22.19223410212
Median: mb = 14.4832748358
Median: mc = 10.4166333328

Inradius: r = 3.09882344333
Circumradius: R = 12.27772297151

Vertex coordinates: A[24; 0] B[0; 0] C[4.14658333333; 6.84219343736]
Centroid: CG[9.38219444444; 2.28106447912]
Coordinates of the circumscribed circle: U[12; -2.59442955648]
Coordinates of the inscribed circle: I[5.5; 3.09882344333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.9865562437° = 160°59'8″ = 0.33218645409 rad
∠ B' = β' = 121.2143542288° = 121°12'49″ = 1.02660172427 rad
∠ C' = γ' = 77.80108952757° = 77°48'3″ = 1.784371087 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    