6 25 25 triangle

Acute isosceles triangle.

Sides: a = 6   b = 25   c = 25

Area: T = 74.45880418759
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 13.78442051587° = 13°47'3″ = 0.24105797648 rad
Angle ∠ B = β = 83.10878974207° = 83°6'28″ = 1.45105064444 rad
Angle ∠ C = γ = 83.10878974207° = 83°6'28″ = 1.45105064444 rad

Height: ha = 24.8199347292
Height: hb = 5.95766433501
Height: hc = 5.95766433501

Median: ma = 24.8199347292
Median: mb = 13.22003787824
Median: mc = 13.22003787824

Inradius: r = 2.65992157813
Circumradius: R = 12.59109838129

Vertex coordinates: A[25; 0] B[0; 0] C[0.72; 5.95766433501]
Centroid: CG[8.57333333333; 1.98655477834]
Coordinates of the circumscribed circle: U[12.5; 1.51109180575]
Coordinates of the inscribed circle: I[3; 2.65992157813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.2165794841° = 166°12'57″ = 0.24105797648 rad
∠ B' = β' = 96.89221025793° = 96°53'32″ = 1.45105064444 rad
∠ C' = γ' = 96.89221025793° = 96°53'32″ = 1.45105064444 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 = 6 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 6+25+25 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-6)(28-25)(28-25) } ; ; T = sqrt{ 5544 } = 74.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.46 }{ 6 } = 24.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.46 }{ 25 } = 5.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.46 }{ 25 } = 5.96 ; ;

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{ 6**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 13° 47'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-6**2-25**2 }{ 2 * 6 * 25 } ) = 83° 6'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-6**2-25**2 }{ 2 * 25 * 6 } ) = 83° 6'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.46 }{ 28 } = 2.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 47'3" } = 12.59 ; ;




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