25 30 30 triangle

Acute isosceles triangle.

Sides: a = 25   b = 30   c = 30

Area: T = 340.8977253582
Perimeter: p = 85
Semiperimeter: s = 42.5

Angle ∠ A = α = 49.24986367043° = 49°14'55″ = 0.86595508626 rad
Angle ∠ B = β = 65.37656816478° = 65°22'32″ = 1.14110208955 rad
Angle ∠ C = γ = 65.37656816478° = 65°22'32″ = 1.14110208955 rad

Height: ha = 27.27217802866
Height: hb = 22.72664835722
Height: hc = 22.72664835722

Median: ma = 27.27217802866
Median: mb = 23.18440462387
Median: mc = 23.18440462387

Inradius: r = 8.0211111849
Circumradius: R = 16.50105729465

Vertex coordinates: A[30; 0] B[0; 0] C[10.41766666667; 22.72664835722]
Centroid: CG[13.47222222222; 7.57554945241]
Coordinates of the circumscribed circle: U[15; 6.87552387277]
Coordinates of the inscribed circle: I[12.5; 8.0211111849]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.7511363296° = 130°45'5″ = 0.86595508626 rad
∠ B' = β' = 114.6244318352° = 114°37'28″ = 1.14110208955 rad
∠ C' = γ' = 114.6244318352° = 114°37'28″ = 1.14110208955 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 = 30 ; ; c = 30 ; ;

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

p = a+b+c = 25+30+30 = 85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 85 }{ 2 } = 42.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42.5 * (42.5-25)(42.5-30)(42.5-30) } ; ; T = sqrt{ 116210.94 } = 340.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 340.9 }{ 25 } = 27.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 340.9 }{ 30 } = 22.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 340.9 }{ 30 } = 22.73 ; ;

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**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 49° 14'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 65° 22'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-25**2-30**2 }{ 2 * 30 * 25 } ) = 65° 22'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 340.9 }{ 42.5 } = 8.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 49° 14'55" } = 16.5 ; ;




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