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

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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.

a = 6 ; ; b = 10 ; ; c = 15 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6+10+15 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-6)(15.5-10)(15.5-15) } ; ; T = sqrt{ 404.94 } = 20.12 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.12 }{ 6 } = 6.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.12 }{ 10 } = 4.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.12 }{ 15 } = 2.68 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6**2-10**2-15**2 }{ 2 * 10 * 15 } ) = 15° 33'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-6**2-15**2 }{ 2 * 6 * 15 } ) = 26° 33'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-6**2-10**2 }{ 2 * 10 * 6 } ) = 137° 52'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.12 }{ 15.5 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 15° 33'49" } = 11.18 ; ;




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