17 25 25 triangle

Acute isosceles triangle.

Sides: a = 17   b = 25   c = 25

Area: T = 199.8440405074
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 39.75437481402° = 39°45'13″ = 0.69438337951 rad
Angle ∠ B = β = 70.12331259299° = 70°7'23″ = 1.22438794293 rad
Angle ∠ C = γ = 70.12331259299° = 70°7'23″ = 1.22438794293 rad

Height: ha = 23.5110635891
Height: hb = 15.98772324059
Height: hc = 15.98772324059

Median: ma = 23.5110635891
Median: mb = 17.3422145196
Median: mc = 17.3422145196

Inradius: r = 5.96553852261
Circumradius: R = 13.29218565643

Vertex coordinates: A[25; 0] B[0; 0] C[5.78; 15.98772324059]
Centroid: CG[10.26; 5.32990774686]
Coordinates of the circumscribed circle: U[12.5; 4.51992312319]
Coordinates of the inscribed circle: I[8.5; 5.96553852261]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.246625186° = 140°14'47″ = 0.69438337951 rad
∠ B' = β' = 109.877687407° = 109°52'37″ = 1.22438794293 rad
∠ C' = γ' = 109.877687407° = 109°52'37″ = 1.22438794293 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 = 17 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 17+25+25 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-17)(33.5-25)(33.5-25) } ; ; T = sqrt{ 39936.19 } = 199.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 199.84 }{ 17 } = 23.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 199.84 }{ 25 } = 15.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 199.84 }{ 25 } = 15.99 ; ;

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{ 17**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 39° 45'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 70° 7'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-17**2-25**2 }{ 2 * 25 * 17 } ) = 70° 7'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 199.84 }{ 33.5 } = 5.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 39° 45'13" } = 13.29 ; ;




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