33 56 65 triangle

Right scalene triangle.

Sides: a = 33   b = 56   c = 65

Area: T = 924
Perimeter: p = 154
Semiperimeter: s = 77

Angle ∠ A = α = 30.51102374061° = 30°30'37″ = 0.53325040983 rad
Angle ∠ B = β = 59.49897625939° = 59°29'23″ = 1.03882922285 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 56
Height: hb = 33
Height: hc = 28.43107692308

Median: ma = 58.38802192528
Median: mb = 43.27881700168
Median: mc = 32.5

Inradius: r = 12
Circumradius: R = 32.5

Vertex coordinates: A[65; 0] B[0; 0] C[16.75438461538; 28.43107692308]
Centroid: CG[27.25112820513; 9.47769230769]
Coordinates of the circumscribed circle: U[32.5; 0]
Coordinates of the inscribed circle: I[21; 12]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.4989762594° = 149°29'23″ = 0.53325040983 rad
∠ B' = β' = 120.5110237406° = 120°30'37″ = 1.03882922285 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

a = 33 ; ; b = 56 ; ; c = 65 ; ;

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

p = a+b+c = 33+56+65 = 154 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 154 }{ 2 } = 77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 77 * (77-33)(77-56)(77-65) } ; ; T = sqrt{ 853776 } = 924 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 924 }{ 33 } = 56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 924 }{ 56 } = 33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 924 }{ 65 } = 28.43 ; ;

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{ 33**2-56**2-65**2 }{ 2 * 56 * 65 } ) = 30° 30'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 56**2-33**2-65**2 }{ 2 * 33 * 65 } ) = 59° 29'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 65**2-33**2-56**2 }{ 2 * 56 * 33 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 924 }{ 77 } = 12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33 }{ 2 * sin 30° 30'37" } = 32.5 ; ;




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