4 25 25 triangle

Acute isosceles triangle.

Sides: a = 4   b = 25   c = 25

Area: T = 49.84397431775
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 9.17771314716° = 9°10'38″ = 0.16601711601 rad
Angle ∠ B = β = 85.41114342642° = 85°24'41″ = 1.49107107468 rad
Angle ∠ C = γ = 85.41114342642° = 85°24'41″ = 1.49107107468 rad

Height: ha = 24.92198715888
Height: hb = 3.98771794542
Height: hc = 3.98771794542

Median: ma = 24.92198715888
Median: mb = 12.8166005618
Median: mc = 12.8166005618

Inradius: r = 1.8465916414
Circumradius: R = 12.54401930298

Vertex coordinates: A[25; 0] B[0; 0] C[0.32; 3.98771794542]
Centroid: CG[8.44; 1.32990598181]
Coordinates of the circumscribed circle: U[12.5; 1.00332154424]
Coordinates of the inscribed circle: I[2; 1.8465916414]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.8232868528° = 170°49'22″ = 0.16601711601 rad
∠ B' = β' = 94.58985657358° = 94°35'19″ = 1.49107107468 rad
∠ C' = γ' = 94.58985657358° = 94°35'19″ = 1.49107107468 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 = 4 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 4+25+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-4)(27-25)(27-25) } ; ; T = sqrt{ 2484 } = 49.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.84 }{ 4 } = 24.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.84 }{ 25 } = 3.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.84 }{ 25 } = 3.99 ; ;

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{ 4**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 9° 10'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-4**2-25**2 }{ 2 * 4 * 25 } ) = 85° 24'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-4**2-25**2 }{ 2 * 25 * 4 } ) = 85° 24'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.84 }{ 27 } = 1.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 10'38" } = 12.54 ; ;




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