7 25 25 triangle

Acute isosceles triangle.

Sides: a = 7   b = 25   c = 25

Area: T = 86.63882565614
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 16.09656924946° = 16°5'44″ = 0.28109228294 rad
Angle ∠ B = β = 81.95221537527° = 81°57'8″ = 1.43303349121 rad
Angle ∠ C = γ = 81.95221537527° = 81°57'8″ = 1.43303349121 rad

Height: ha = 24.7543787589
Height: hb = 6.93110605249
Height: hc = 6.93110605249

Median: ma = 24.7543787589
Median: mb = 13.44443296597
Median: mc = 13.44443296597

Inradius: r = 3.04399388267
Circumradius: R = 12.62443306757

Vertex coordinates: A[25; 0] B[0; 0] C[0.98; 6.93110605249]
Centroid: CG[8.66; 2.31103535083]
Coordinates of the circumscribed circle: U[12.5; 1.76774062946]
Coordinates of the inscribed circle: I[3.5; 3.04399388267]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.9044307505° = 163°54'16″ = 0.28109228294 rad
∠ B' = β' = 98.04878462473° = 98°2'52″ = 1.43303349121 rad
∠ C' = γ' = 98.04878462473° = 98°2'52″ = 1.43303349121 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 = 7 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 7+25+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-7)(28.5-25)(28.5-25) } ; ; T = sqrt{ 7506.19 } = 86.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.64 }{ 7 } = 24.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.64 }{ 25 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.64 }{ 25 } = 6.93 ; ;

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{ 7**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 16° 5'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 81° 57'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-25**2 }{ 2 * 25 * 7 } ) = 81° 57'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.64 }{ 28.5 } = 3.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 5'44" } = 12.62 ; ;




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