1 15 15 triangle

Acute isosceles triangle.

Sides: a = 1   b = 15   c = 15

Area: T = 7.49658321753
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 3.82204263434° = 3°49'14″ = 0.06766790185 rad
Angle ∠ B = β = 88.09897868283° = 88°5'23″ = 1.53774568175 rad
Angle ∠ C = γ = 88.09897868283° = 88°5'23″ = 1.53774568175 rad

Height: ha = 14.99216643506
Height: hb = 0.999944429
Height: hc = 0.999944429

Median: ma = 14.99216643506
Median: mb = 7.53332595867
Median: mc = 7.53332595867

Inradius: r = 0.48436020758
Circumradius: R = 7.50441701421

Vertex coordinates: A[15; 0] B[0; 0] C[0.03333333333; 0.999944429]
Centroid: CG[5.01111111111; 0.33331480967]
Coordinates of the circumscribed circle: U[7.5; 0.25501390047]
Coordinates of the inscribed circle: I[0.5; 0.48436020758]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.1879573657° = 176°10'46″ = 0.06766790185 rad
∠ B' = β' = 91.91102131717° = 91°54'37″ = 1.53774568175 rad
∠ C' = γ' = 91.91102131717° = 91°54'37″ = 1.53774568175 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 = 1 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 1+15+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 * (15.5-1)(15.5-15)(15.5-15) } ; ; T = sqrt{ 56.19 } = 7.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.5 }{ 1 } = 14.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.5 }{ 15 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.5 }{ 15 } = 1 ; ;

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{ 1**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 3° 49'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-1**2-15**2 }{ 2 * 1 * 15 } ) = 88° 5'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-1**2-15**2 }{ 2 * 15 * 1 } ) = 88° 5'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.5 }{ 15.5 } = 0.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 3° 49'14" } = 7.5 ; ;




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