3 25 25 triangle

Acute isosceles triangle.

Sides: a = 3   b = 25   c = 25

Area: T = 37.43224391404
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 6.8879625535° = 6°52'47″ = 0.12200721169 rad
Angle ∠ B = β = 86.56601872325° = 86°33'37″ = 1.51107602683 rad
Angle ∠ C = γ = 86.56601872325° = 86°33'37″ = 1.51107602683 rad

Height: ha = 24.95549594269
Height: hb = 2.99545951312
Height: hc = 2.99545951312

Median: ma = 24.95549594269
Median: mb = 12.67987223331
Median: mc = 12.67987223331

Inradius: r = 1.41325448732
Circumradius: R = 12.52325609328

Vertex coordinates: A[25; 0] B[0; 0] C[0.18; 2.99545951312]
Centroid: CG[8.39333333333; 0.99881983771]
Coordinates of the circumscribed circle: U[12.5; 0.7511353656]
Coordinates of the inscribed circle: I[1.5; 1.41325448732]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.1220374465° = 173°7'13″ = 0.12200721169 rad
∠ B' = β' = 93.44398127675° = 93°26'23″ = 1.51107602683 rad
∠ C' = γ' = 93.44398127675° = 93°26'23″ = 1.51107602683 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 = 3 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 3+25+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-3)(26.5-25)(26.5-25) } ; ; T = sqrt{ 1401.19 } = 37.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.43 }{ 3 } = 24.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.43 }{ 25 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.43 }{ 25 } = 2.99 ; ;

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{ 3**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 6° 52'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-3**2-25**2 }{ 2 * 3 * 25 } ) = 86° 33'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-3**2-25**2 }{ 2 * 25 * 3 } ) = 86° 33'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.43 }{ 26.5 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 52'47" } = 12.52 ; ;




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