10 11 15 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 11   c = 15

Area: T = 54.99109083395
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 41.80218441931° = 41°48'7″ = 0.73295798146 rad
Angle ∠ B = β = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ C = γ = 91.04217988505° = 91°2'30″ = 1.58989791469 rad

Height: ha = 10.99881816679
Height: hb = 9.99883469708
Height: hc = 7.33221211119

Median: ma = 12.16655250606
Median: mb = 11.5
Median: mc = 7.36554599313

Inradius: r = 3.05550504633
Circumradius: R = 7.50112399769

Vertex coordinates: A[15; 0] B[0; 0] C[6.8; 7.33221211119]
Centroid: CG[7.26766666667; 2.44440403706]
Coordinates of the circumscribed circle: U[7.5; -0.13663861814]
Coordinates of the inscribed circle: I[7; 3.05550504633]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.1988155807° = 138°11'53″ = 0.73295798146 rad
∠ B' = β' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ C' = γ' = 88.95882011495° = 88°57'30″ = 1.58989791469 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 = 10 ; ; b = 11 ; ; c = 15 ; ;

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

p = a+b+c = 10+11+15 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-10)(18-11)(18-15) } ; ; T = sqrt{ 3024 } = 54.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.99 }{ 10 } = 11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.99 }{ 11 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.99 }{ 15 } = 7.33 ; ;

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{ 10**2-11**2-15**2 }{ 2 * 11 * 15 } ) = 41° 48'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-10**2-15**2 }{ 2 * 10 * 15 } ) = 47° 9'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-10**2-11**2 }{ 2 * 11 * 10 } ) = 91° 2'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.99 }{ 18 } = 3.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 41° 48'7" } = 7.5 ; ;




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