# 7 10 15 triangle

### Obtuse scalene triangle.

Sides: a = 7   b = 10   c = 15

Area: T = 29.39438769134
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ C = γ = 122.8788349564° = 122°52'42″ = 2.14546317793 rad

Height: ha = 8.39882505467
Height: hb = 5.87987753827
Height: hc = 3.91991835885

Median: ma = 12.25876506721
Median: mb = 10.58330052443
Median: mc = 4.27220018727

Inradius: r = 1.83771173071
Circumradius: R = 8.93304313539

Vertex coordinates: A[15; 0] B[0; 0] C[5.8; 3.91991835885]
Centroid: CG[6.93333333333; 1.30663945295]
Coordinates of the circumscribed circle: U[7.5; -4.84879484493]
Coordinates of the inscribed circle: I[6; 1.83771173071]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ C' = γ' = 57.12216504356° = 57°7'18″ = 2.14546317793 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    