150 150 130 triangle

Acute isosceles triangle.

Sides: a = 150   b = 150   c = 130

Area: T = 8787.029879249
Perimeter: p = 430
Semiperimeter: s = 215

Angle ∠ A = α = 64.32107113805° = 64°19'15″ = 1.12326081908 rad
Angle ∠ B = β = 64.32107113805° = 64°19'15″ = 1.12326081908 rad
Angle ∠ C = γ = 51.35985772389° = 51°21'31″ = 0.8966376272 rad

Height: ha = 117.16603839
Height: hb = 117.16603839
Height: hc = 135.1855058346

Median: ma = 118.6388105177
Median: mb = 118.6388105177
Median: mc = 135.1855058346

Inradius: r = 40.87699013604
Circumradius: R = 83.21992561637

Vertex coordinates: A[130; 0] B[0; 0] C[65; 135.1855058346]
Centroid: CG[65; 45.06216861153]
Coordinates of the circumscribed circle: U[65; 51.96658021822]
Coordinates of the inscribed circle: I[65; 40.87699013604]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.6799288619° = 115°40'45″ = 1.12326081908 rad
∠ B' = β' = 115.6799288619° = 115°40'45″ = 1.12326081908 rad
∠ C' = γ' = 128.6411422761° = 128°38'29″ = 0.8966376272 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 = 150 ; ; b = 150 ; ; c = 130 ; ;

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

p = a+b+c = 150+150+130 = 430 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 430 }{ 2 } = 215 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 215 * (215-150)(215-150)(215-130) } ; ; T = sqrt{ 77211875 } = 8787.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8787.03 }{ 150 } = 117.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8787.03 }{ 150 } = 117.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8787.03 }{ 130 } = 135.19 ; ;

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{ 150**2-150**2-130**2 }{ 2 * 150 * 130 } ) = 64° 19'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 150**2-150**2-130**2 }{ 2 * 150 * 130 } ) = 64° 19'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 130**2-150**2-150**2 }{ 2 * 150 * 150 } ) = 51° 21'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8787.03 }{ 215 } = 40.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 150 }{ 2 * sin 64° 19'15" } = 83.22 ; ;




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