# 10 24 30 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 24   c = 30

Area: T = 106.1321993291
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 17.14662099989° = 17°8'46″ = 0.29992578187 rad
Angle ∠ B = β = 45.03656507165° = 45°2'8″ = 0.78660203858 rad
Angle ∠ C = γ = 117.8188139285° = 117°49'5″ = 2.05663144491 rad

Height: ha = 21.22663986583
Height: hb = 8.84443327743
Height: hc = 7.07554662194

Median: ma = 26.70220598456
Median: mb = 18.86879622641
Median: mc = 10.63301458127

Inradius: r = 3.31766247904
Circumradius: R = 16.96600131325

Vertex coordinates: A[30; 0] B[0; 0] C[7.06766666667; 7.07554662194]
Centroid: CG[12.35655555556; 2.35884887398]
Coordinates of the circumscribed circle: U[15; -7.91546727952]
Coordinates of the inscribed circle: I[8; 3.31766247904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.8543790001° = 162°51'14″ = 0.29992578187 rad
∠ B' = β' = 134.9644349284° = 134°57'52″ = 0.78660203858 rad
∠ C' = γ' = 62.18218607153° = 62°10'55″ = 2.05663144491 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    