15 15 29 triangle

Obtuse isosceles triangle.

Sides: a = 15   b = 15   c = 29

Area: T = 55.6888306672
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 14.8355111582° = 14°50'6″ = 0.2598921542 rad
Angle ∠ B = β = 14.8355111582° = 14°50'6″ = 0.2598921542 rad
Angle ∠ C = γ = 150.3329776836° = 150°19'47″ = 2.62437495696 rad

Height: ha = 7.42551075563
Height: hb = 7.42551075563
Height: hc = 3.84105728739

Median: ma = 21.83546055609
Median: mb = 21.83546055609
Median: mc = 3.84105728739

Inradius: r = 1.88877392092
Circumradius: R = 29.29325049707

Vertex coordinates: A[29; 0] B[0; 0] C[14.5; 3.84105728739]
Centroid: CG[14.5; 1.2880190958]
Coordinates of the circumscribed circle: U[14.5; -25.45219320968]
Coordinates of the inscribed circle: I[14.5; 1.88877392092]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.1654888418° = 165°9'54″ = 0.2598921542 rad
∠ B' = β' = 165.1654888418° = 165°9'54″ = 0.2598921542 rad
∠ C' = γ' = 29.6770223164° = 29°40'13″ = 2.62437495696 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 = 29 ; ;

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

p = a+b+c = 15+15+29 = 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)(29.5-15)(29.5-29) } ; ; T = sqrt{ 3101.19 } = 55.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.69 }{ 15 } = 7.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.69 }{ 15 } = 7.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.69 }{ 29 } = 3.84 ; ;

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**2-29**2 }{ 2 * 15 * 29 } ) = 14° 50'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 14° 50'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 150° 19'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.69 }{ 29.5 } = 1.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 14° 50'6" } = 29.29 ; ;




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