8 9 15 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 9   c = 15

Area: T = 29.93332590942
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 26.32545765375° = 26°19'28″ = 0.45994505348 rad
Angle ∠ B = β = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ C = γ = 123.7498988596° = 123°44'56″ = 2.1659827297 rad

Height: ha = 7.48333147735
Height: hb = 6.65218353543
Height: hc = 3.99111012126

Median: ma = 11.70546999107
Median: mb = 11.14767484048
Median: mc = 4.03111288741

Inradius: r = 1.87108286934
Circumradius: R = 9.02200669145

Vertex coordinates: A[15; 0] B[0; 0] C[6.93333333333; 3.99111012126]
Centroid: CG[7.31111111111; 1.33303670709]
Coordinates of the circumscribed circle: U[7.5; -5.01111482859]
Coordinates of the inscribed circle: I[7; 1.87108286934]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6755423463° = 153°40'32″ = 0.45994505348 rad
∠ B' = β' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ C' = γ' = 56.25110114041° = 56°15'4″ = 2.1659827297 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 = 8 ; ; b = 9 ; ; c = 15 ; ;

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

p = a+b+c = 8+9+15 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-8)(16-9)(16-15) } ; ; T = sqrt{ 896 } = 29.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.93 }{ 8 } = 7.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.93 }{ 9 } = 6.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.93 }{ 15 } = 3.99 ; ;

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{ 8**2-9**2-15**2 }{ 2 * 9 * 15 } ) = 26° 19'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-8**2-15**2 }{ 2 * 8 * 15 } ) = 29° 55'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-8**2-9**2 }{ 2 * 9 * 8 } ) = 123° 44'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.93 }{ 16 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 26° 19'28" } = 9.02 ; ;




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