25 25 30 triangle

Acute isosceles triangle.

Sides: a = 25   b = 25   c = 30

Area: T = 300
Perimeter: p = 80
Semiperimeter: s = 40

Angle ∠ A = α = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 73.74397952917° = 73°44'23″ = 1.28770022176 rad

Height: ha = 24
Height: hb = 24
Height: hc = 20

Median: ma = 24.62221445045
Median: mb = 24.62221445045
Median: mc = 20

Inradius: r = 7.5
Circumradius: R = 15.625

Vertex coordinates: A[30; 0] B[0; 0] C[15; 20]
Centroid: CG[15; 6.66766666667]
Coordinates of the circumscribed circle: U[15; 4.375]
Coordinates of the inscribed circle: I[15; 7.5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 106.2660204708° = 106°15'37″ = 1.28770022176 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 = 25 ; ; b = 25 ; ; c = 30 ; ;

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

p = a+b+c = 25+25+30 = 80 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 80 }{ 2 } = 40 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40 * (40-25)(40-25)(40-30) } ; ; T = sqrt{ 90000 } = 300 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 300 }{ 25 } = 24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 300 }{ 25 } = 24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 300 }{ 30 } = 20 ; ;

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{ 25**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 53° 7'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 73° 44'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 300 }{ 40 } = 7.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 53° 7'48" } = 15.63 ; ;




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