8 25 25 triangle

Acute isosceles triangle.

Sides: a = 8   b = 25   c = 25

Area: T = 98.7121701434
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 18.41437924427° = 18°24'50″ = 0.32113813059 rad
Angle ∠ B = β = 80.79331037787° = 80°47'35″ = 1.41101056738 rad
Angle ∠ C = γ = 80.79331037787° = 80°47'35″ = 1.41101056738 rad

Height: ha = 24.67879253585
Height: hb = 7.89769361147
Height: hc = 7.89769361147

Median: ma = 24.67879253585
Median: mb = 13.7220422734
Median: mc = 13.7220422734

Inradius: r = 3.40438517736
Circumradius: R = 12.66331390386

Vertex coordinates: A[25; 0] B[0; 0] C[1.28; 7.89769361147]
Centroid: CG[8.76; 2.63223120382]
Coordinates of the circumscribed circle: U[12.5; 2.02661022462]
Coordinates of the inscribed circle: I[4; 3.40438517736]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5866207557° = 161°35'10″ = 0.32113813059 rad
∠ B' = β' = 99.20768962213° = 99°12'25″ = 1.41101056738 rad
∠ C' = γ' = 99.20768962213° = 99°12'25″ = 1.41101056738 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 = 8 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 8+25+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-8)(29-25)(29-25) } ; ; T = sqrt{ 9744 } = 98.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.71 }{ 8 } = 24.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.71 }{ 25 } = 7.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.71 }{ 25 } = 7.9 ; ;

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{ 8**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 18° 24'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-8**2-25**2 }{ 2 * 8 * 25 } ) = 80° 47'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-8**2-25**2 }{ 2 * 25 * 8 } ) = 80° 47'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.71 }{ 29 } = 3.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 18° 24'50" } = 12.66 ; ;




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