2 15 15 triangle

Acute isosceles triangle.

Sides: a = 2   b = 15   c = 15

Area: T = 14.96766295471
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 7.64551074586° = 7°38'42″ = 0.13334322968 rad
Angle ∠ B = β = 86.17774462707° = 86°10'39″ = 1.50440801784 rad
Angle ∠ C = γ = 86.17774462707° = 86°10'39″ = 1.50440801784 rad

Height: ha = 14.96766295471
Height: hb = 1.99655506063
Height: hc = 1.99655506063

Median: ma = 14.96766295471
Median: mb = 7.63221687612
Median: mc = 7.63221687612

Inradius: r = 0.93554143467
Circumradius: R = 7.51767224288

Vertex coordinates: A[15; 0] B[0; 0] C[0.13333333333; 1.99655506063]
Centroid: CG[5.04444444444; 0.66551835354]
Coordinates of the circumscribed circle: U[7.5; 0.50111148286]
Coordinates of the inscribed circle: I[1; 0.93554143467]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.3554892541° = 172°21'18″ = 0.13334322968 rad
∠ B' = β' = 93.82325537293° = 93°49'21″ = 1.50440801784 rad
∠ C' = γ' = 93.82325537293° = 93°49'21″ = 1.50440801784 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 = 2 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 2+15+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 * (16-2)(16-15)(16-15) } ; ; T = sqrt{ 224 } = 14.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.97 }{ 2 } = 14.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.97 }{ 15 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.97 }{ 15 } = 2 ; ;

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{ 2**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 7° 38'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-2**2-15**2 }{ 2 * 2 * 15 } ) = 86° 10'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-2**2-15**2 }{ 2 * 15 * 2 } ) = 86° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.97 }{ 16 } = 0.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 7° 38'42" } = 7.52 ; ;




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