# 6 10 15 triangle

### Obtuse scalene triangle.

Sides: a = 6   b = 10   c = 15

Area: T = 20.12330589126
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 15.56435751871° = 15°33'49″ = 0.27216356304 rad
Angle ∠ B = β = 26.56328406278° = 26°33'46″ = 0.46436090276 rad
Angle ∠ C = γ = 137.8743584185° = 137°52'25″ = 2.40663479956 rad

Height: ha = 6.70876863042
Height: hb = 4.02546117825
Height: hc = 2.68330745217

Median: ma = 12.39895116934
Median: mb = 10.27113192921
Median: mc = 3.42878273002

Inradius: r = 1.29882618653
Circumradius: R = 11.18112026679

Vertex coordinates: A[15; 0] B[0; 0] C[5.36766666667; 2.68330745217]
Centroid: CG[6.78988888889; 0.89443581739]
Coordinates of the circumscribed circle: U[7.5; -8.2932725312]
Coordinates of the inscribed circle: I[5.5; 1.29882618653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.4366424813° = 164°26'11″ = 0.27216356304 rad
∠ B' = β' = 153.4377159372° = 153°26'14″ = 0.46436090276 rad
∠ C' = γ' = 42.12664158149° = 42°7'35″ = 2.40663479956 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    