15 17 27 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 27

Area: T = 115.6176553746
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 30.25501231211° = 30°15' = 0.52879642476 rad
Angle ∠ B = β = 34.81662157084° = 34°48'58″ = 0.60876575972 rad
Angle ∠ C = γ = 114.934366117° = 114°56'1″ = 2.00659708088 rad

Height: ha = 15.41655404994
Height: hb = 13.60219474995
Height: hc = 8.56441891663

Median: ma = 21.2787922831
Median: mb = 20.11883995387
Median: mc = 8.64658082329

Inradius: r = 3.91992052117
Circumradius: R = 14.88875740042

Vertex coordinates: A[27; 0] B[0; 0] C[12.31548148148; 8.56441891663]
Centroid: CG[13.10549382716; 2.85547297221]
Coordinates of the circumscribed circle: U[13.5; -6.2766134139]
Coordinates of the inscribed circle: I[12.5; 3.91992052117]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.7549876879° = 149°45' = 0.52879642476 rad
∠ B' = β' = 145.1843784292° = 145°11'2″ = 0.60876575972 rad
∠ C' = γ' = 65.06663388295° = 65°3'59″ = 2.00659708088 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 = 15 ; ; b = 17 ; ; c = 27 ; ;

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

p = a+b+c = 15+17+27 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-15)(29.5-17)(29.5-27) } ; ; T = sqrt{ 13367.19 } = 115.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 115.62 }{ 15 } = 15.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 115.62 }{ 17 } = 13.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 115.62 }{ 27 } = 8.56 ; ;

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{ 15**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 30° 15' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 34° 48'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 114° 56'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 115.62 }{ 29.5 } = 3.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 30° 15' } = 14.89 ; ;




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