11 25 25 triangle

Acute isosceles triangle.

Sides: a = 11   b = 25   c = 25

Area: T = 134.1311232381
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 25.41880659888° = 25°25'5″ = 0.4443628941 rad
Angle ∠ B = β = 77.29109670056° = 77°17'27″ = 1.34989818563 rad
Angle ∠ C = γ = 77.29109670056° = 77°17'27″ = 1.34989818563 rad

Height: ha = 24.38774967965
Height: hb = 10.73304985905
Height: hc = 10.73304985905

Median: ma = 24.38774967965
Median: mb = 14.72224318643
Median: mc = 14.72224318643

Inradius: r = 4.3987745324
Circumradius: R = 12.81439432516

Vertex coordinates: A[25; 0] B[0; 0] C[2.42; 10.73304985905]
Centroid: CG[9.14; 3.57768328635]
Coordinates of the circumscribed circle: U[12.5; 2.81990675154]
Coordinates of the inscribed circle: I[5.5; 4.3987745324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.5821934011° = 154°34'55″ = 0.4443628941 rad
∠ B' = β' = 102.7099032994° = 102°42'33″ = 1.34989818563 rad
∠ C' = γ' = 102.7099032994° = 102°42'33″ = 1.34989818563 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 = 11 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 11+25+25 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-11)(30.5-25)(30.5-25) } ; ; T = sqrt{ 17991.19 } = 134.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.13 }{ 11 } = 24.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.13 }{ 25 } = 10.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.13 }{ 25 } = 10.73 ; ;

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{ 11**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 25° 25'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 77° 17'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-25**2 }{ 2 * 25 * 11 } ) = 77° 17'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.13 }{ 30.5 } = 4.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 25° 25'5" } = 12.81 ; ;




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