# 15 21 24 triangle

### Acute scalene triangle.

Sides: a = 15   b = 21   c = 24

Area: T = 155.8854572681
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 20.78546096908
Height: hb = 14.84661497792
Height: hc = 12.99903810568

Median: ma = 21.26661703181
Median: mb = 17.03767250374
Median: mc = 13.74877270849

Inradius: r = 5.19661524227
Circumradius: R = 12.1244355653

Vertex coordinates: A[24; 0] B[0; 0] C[7.5; 12.99903810568]
Centroid: CG[10.5; 4.33301270189]
Coordinates of the circumscribed circle: U[12; 1.73220508076]
Coordinates of the inscribed circle: I[9; 5.19661524227]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 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.