150 60 137.477 triangle

Right scalene triangle.

Sides: a = 150   b = 60   c = 137.477

Area: T = 4124.310999996
Perimeter: p = 347.477
Semiperimeter: s = 173.73985

Angle ∠ A = α = 900.0002586417° = 90°1″ = 1.57108008409 rad
Angle ∠ B = β = 23.57881784779° = 23°34'41″ = 0.41215168461 rad
Angle ∠ C = γ = 66.42215628804° = 66°25'18″ = 1.15992749666 rad

Height: ha = 54.99107999994
Height: hb = 137.4776999999
Height: hc = 609.9999999994

Median: ma = 754.9997517629
Median: mb = 140.7122340484
Median: mc = 91.24215399791

Inradius: r = 23.73986071594
Circumradius: R = 755.0000000008

Vertex coordinates: A[137.477; 0] B[0; 0] C[137.4777270849; 609.9999999994]
Centroid: CG[91.65114236163; 209.9999999998]
Coordinates of the circumscribed circle: U[68.73985; 300.0003102961]
Coordinates of the inscribed circle: I[113.73985; 23.73986071594]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 909.9997413583° = 89°59'59″ = 1.57108008409 rad
∠ B' = β' = 156.4221821522° = 156°25'19″ = 0.41215168461 rad
∠ C' = γ' = 113.578843712° = 113°34'42″ = 1.15992749666 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 = 60 ; ; c = 137.48 ; ;

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

p = a+b+c = 150+60+137.48 = 347.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 347.48 }{ 2 } = 173.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 173.74 * (173.74-150)(173.74-60)(173.74-137.48) } ; ; T = sqrt{ 17009932.98 } = 4124.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4124.31 }{ 150 } = 54.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4124.31 }{ 60 } = 137.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4124.31 }{ 137.48 } = 60 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 60**2+137.48**2-150**2 }{ 2 * 60 * 137.48 } ) = 90° 1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 150**2+137.48**2-60**2 }{ 2 * 150 * 137.48 } ) = 23° 34'41" ; ; gamma = 180° - alpha - beta = 180° - 90° 1" - 23° 34'41" = 66° 25'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4124.31 }{ 173.74 } = 23.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 150 }{ 2 * sin 90° 1" } = 75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 137.48**2 - 150**2 } }{ 2 } = 75 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 137.48**2+2 * 150**2 - 60**2 } }{ 2 } = 140.712 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 150**2 - 137.48**2 } }{ 2 } = 91.242 ; ;
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