947.06 150 958.88 triangle

Obtuse scalene triangle.

Sides: a = 947.06   b = 150   c = 958.88

Area: T = 71029.54996499
Perimeter: p = 2055.94
Semiperimeter: s = 1027.97

Angle ∠ A = α = 80.99444247266° = 80°59'40″ = 1.41436193872 rad
Angle ∠ B = β = 98.9998862295° = 9° = 0.1577077647 rad
Angle ∠ C = γ = 90.00656890439° = 90°20″ = 1.57108956193 rad

Height: ha = 1509.999999261
Height: hb = 947.0659995331
Height: hc = 148.1510967065

Median: ma = 496.7344100199
Median: mb = 950.0322498918
Median: mc = 479.4255289487

Inradius: r = 69.09768604627
Circumradius: R = 479.4440002363

Vertex coordinates: A[958.88; 0] B[0; 0] C[935.4400414025; 148.1510967065]
Centroid: CG[631.4276804675; 49.38436556885]
Coordinates of the circumscribed circle: U[479.44; -0.04876048192]
Coordinates of the inscribed circle: I[877.97; 69.09768604627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.00655752734° = 99°20″ = 1.41436193872 rad
∠ B' = β' = 1711.00011377° = 171° = 0.1577077647 rad
∠ C' = γ' = 89.99443109561° = 89°59'40″ = 1.57108956193 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 = 947.06 ; ; b = 150 ; ; c = 958.88 ; ;

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

p = a+b+c = 947.06+150+958.88 = 2055.94 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2055.94 }{ 2 } = 1027.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1027.97 * (1027.97-947.06)(1027.97-150)(1027.97-958.88) } ; ; T = sqrt{ 5045189820.51 } = 71029.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71029.5 }{ 947.06 } = 150 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71029.5 }{ 150 } = 947.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71029.5 }{ 958.88 } = 148.15 ; ;

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{ 947.06**2-150**2-958.88**2 }{ 2 * 150 * 958.88 } ) = 80° 59'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 150**2-947.06**2-958.88**2 }{ 2 * 947.06 * 958.88 } ) = 9° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 958.88**2-947.06**2-150**2 }{ 2 * 150 * 947.06 } ) = 90° 20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71029.5 }{ 1027.97 } = 69.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 947.06 }{ 2 * sin 80° 59'40" } = 479.44 ; ;




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