7 9 15 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 9   c = 15

Area: T = 20.69326919467
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 17.85219455267° = 17°51'7″ = 0.31215752273 rad
Angle ∠ B = β = 23.2132754908° = 23°12'46″ = 0.40551390016 rad
Angle ∠ C = γ = 138.9355299565° = 138°56'7″ = 2.42548784247 rad

Height: ha = 5.91221976991
Height: hb = 4.59883759882
Height: hc = 2.75990255929

Median: ma = 11.86438105177
Median: mb = 10.80550913925
Median: mc = 2.95880398915

Inradius: r = 1.33550123837
Circumradius: R = 11.41770742313

Vertex coordinates: A[15; 0] B[0; 0] C[6.43333333333; 2.75990255929]
Centroid: CG[7.14444444444; 0.92196751976]
Coordinates of the circumscribed circle: U[7.5; -8.60881115236]
Coordinates of the inscribed circle: I[6.5; 1.33550123837]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.1488054473° = 162°8'53″ = 0.31215752273 rad
∠ B' = β' = 156.7877245092° = 156°47'14″ = 0.40551390016 rad
∠ C' = γ' = 41.06547004347° = 41°3'53″ = 2.42548784247 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 = 7 ; ; b = 9 ; ; c = 15 ; ;

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

p = a+b+c = 7+9+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 * (15.5-7)(15.5-9)(15.5-15) } ; ; T = sqrt{ 428.19 } = 20.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.69 }{ 7 } = 5.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.69 }{ 9 } = 4.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.69 }{ 15 } = 2.76 ; ;

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{ 7**2-9**2-15**2 }{ 2 * 9 * 15 } ) = 17° 51'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-7**2-15**2 }{ 2 * 7 * 15 } ) = 23° 12'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-7**2-9**2 }{ 2 * 9 * 7 } ) = 138° 56'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.69 }{ 15.5 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 17° 51'7" } = 11.42 ; ;




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