15 17 17 triangle

Acute isosceles triangle.

Sides: a = 15   b = 17   c = 17

Area: T = 114.4211097268
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 52.3587937408° = 52°21'29″ = 0.91438183973 rad
Angle ∠ B = β = 63.8211031296° = 63°49'16″ = 1.11438871281 rad
Angle ∠ C = γ = 63.8211031296° = 63°49'16″ = 1.11438871281 rad

Height: ha = 15.25661463024
Height: hb = 13.46113055609
Height: hc = 13.46113055609

Median: ma = 15.25661463024
Median: mb = 13.59222772191
Median: mc = 13.59222772191

Inradius: r = 4.67702488681
Circumradius: R = 9.47215924412

Vertex coordinates: A[17; 0] B[0; 0] C[6.61876470588; 13.46113055609]
Centroid: CG[7.87325490196; 4.48771018536]
Coordinates of the circumscribed circle: U[8.5; 4.17986437241]
Coordinates of the inscribed circle: I[7.5; 4.67702488681]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.6422062592° = 127°38'31″ = 0.91438183973 rad
∠ B' = β' = 116.1798968704° = 116°10'44″ = 1.11438871281 rad
∠ C' = γ' = 116.1798968704° = 116°10'44″ = 1.11438871281 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 = 17 ; ;

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

p = a+b+c = 15+17+17 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-15)(24.5-17)(24.5-17) } ; ; T = sqrt{ 13092.19 } = 114.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 114.42 }{ 15 } = 15.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 114.42 }{ 17 } = 13.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 114.42 }{ 17 } = 13.46 ; ;

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**2-17**2 }{ 2 * 17 * 17 } ) = 52° 21'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 63° 49'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 63° 49'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 114.42 }{ 24.5 } = 4.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 52° 21'29" } = 9.47 ; ;




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