15 15 25 triangle

Obtuse isosceles triangle.

Sides: a = 15   b = 15   c = 25

Area: T = 103.6454524699
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ C = γ = 112.8855380476° = 112°53'7″ = 1.97702215667 rad

Height: ha = 13.81992699598
Height: hb = 13.81992699598
Height: hc = 8.29215619759

Median: ma = 19.20328643697
Median: mb = 19.20328643697
Median: mc = 8.29215619759

Inradius: r = 3.76988918072
Circumradius: R = 13.5688010506

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 8.29215619759]
Centroid: CG[12.5; 2.7643853992]
Coordinates of the circumscribed circle: U[12.5; -5.27664485301]
Coordinates of the inscribed circle: I[12.5; 3.76988918072]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ C' = γ' = 67.11546195238° = 67°6'53″ = 1.97702215667 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 = 15 ; ; c = 25 ; ;

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

p = a+b+c = 15+15+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-15)(27.5-15)(27.5-25) } ; ; T = sqrt{ 10742.19 } = 103.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.64 }{ 15 } = 13.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.64 }{ 15 } = 13.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.64 }{ 25 } = 8.29 ; ;

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**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 33° 33'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 33° 33'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 112° 53'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.64 }{ 27.5 } = 3.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 33° 33'26" } = 13.57 ; ;




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