15 25 25 triangle

Acute isosceles triangle.

Sides: a = 15   b = 25   c = 25

Area: T = 178.8643600266
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 34.91552062474° = 34°54'55″ = 0.6099385308 rad
Angle ∠ B = β = 72.54223968763° = 72°32'33″ = 1.26661036728 rad
Angle ∠ C = γ = 72.54223968763° = 72°32'33″ = 1.26661036728 rad

Height: ha = 23.84884800354
Height: hb = 14.30990880213
Height: hc = 14.30990880213

Median: ma = 23.84884800354
Median: mb = 16.39435963108
Median: mc = 16.39435963108

Inradius: r = 5.50334953928
Circumradius: R = 13.1043560459

Vertex coordinates: A[25; 0] B[0; 0] C[4.5; 14.30990880213]
Centroid: CG[9.83333333333; 4.77696960071]
Coordinates of the circumscribed circle: U[12.5; 3.93110681377]
Coordinates of the inscribed circle: I[7.5; 5.50334953928]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0854793753° = 145°5'5″ = 0.6099385308 rad
∠ B' = β' = 107.4587603124° = 107°27'27″ = 1.26661036728 rad
∠ C' = γ' = 107.4587603124° = 107°27'27″ = 1.26661036728 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 = 15 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 15+25+25 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-15)(32.5-25)(32.5-25) } ; ; T = sqrt{ 31992.19 } = 178.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 178.86 }{ 15 } = 23.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 178.86 }{ 25 } = 14.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 178.86 }{ 25 } = 14.31 ; ;

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{ 15**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 34° 54'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 72° 32'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-15**2-25**2 }{ 2 * 25 * 15 } ) = 72° 32'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 178.86 }{ 32.5 } = 5.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 34° 54'55" } = 13.1 ; ;




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