12 15 17 triangle

Acute scalene triangle.

Sides: a = 12   b = 15   c = 17

Area: T = 87.75496438739
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 43.4990358347° = 43°29'25″ = 0.7599049946 rad
Angle ∠ B = β = 59.34992300599° = 59°20'57″ = 1.03658394731 rad
Angle ∠ C = γ = 77.16604115931° = 77°9'37″ = 1.34767032345 rad

Height: ha = 14.62549406457
Height: hb = 11.76999525165
Height: hc = 10.32334875146

Median: ma = 14.86660687473
Median: mb = 12.65989889012
Median: mc = 10.59548100502

Inradius: r = 3.98986201761
Circumradius: R = 8.71879840992

Vertex coordinates: A[17; 0] B[0; 0] C[6.11876470588; 10.32334875146]
Centroid: CG[7.70658823529; 3.44111625049]
Coordinates of the circumscribed circle: U[8.5; 1.93773297998]
Coordinates of the inscribed circle: I[7; 3.98986201761]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.5109641653° = 136°30'35″ = 0.7599049946 rad
∠ B' = β' = 120.651076994° = 120°39'3″ = 1.03658394731 rad
∠ C' = γ' = 102.8439588407° = 102°50'23″ = 1.34767032345 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 = 12 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 12+15+17 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-12)(22-15)(22-17) } ; ; T = sqrt{ 7700 } = 87.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87.75 }{ 12 } = 14.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87.75 }{ 15 } = 11.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87.75 }{ 17 } = 10.32 ; ;

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{ 12**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 43° 29'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 59° 20'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-12**2-15**2 }{ 2 * 15 * 12 } ) = 77° 9'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87.75 }{ 22 } = 3.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 43° 29'25" } = 8.72 ; ;




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