13.6 57 58.6 triangle

Right scalene triangle.

Sides: a = 13.6   b = 57   c = 58.6

Area: T = 387.6
Perimeter: p = 129.2
Semiperimeter: s = 64.6

Angle ∠ A = α = 13.42196736155° = 13°25'11″ = 0.23442174891 rad
Angle ∠ B = β = 76.58803263845° = 76°34'49″ = 1.33765788377 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 57
Height: hb = 13.6
Height: hc = 13.2298668942

Median: ma = 57.40441810324
Median: mb = 31.5798632016
Median: mc = 29.3

Inradius: r = 6
Circumradius: R = 29.3

Vertex coordinates: A[58.6; 0] B[0; 0] C[3.15663139932; 13.2298668942]
Centroid: CG[20.58554379977; 4.4109556314]
Coordinates of the circumscribed circle: U[29.3; -0]
Coordinates of the inscribed circle: I[7.6; 6]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.5880326384° = 166°34'49″ = 0.23442174891 rad
∠ B' = β' = 103.4219673616° = 103°25'11″ = 1.33765788377 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

a = 13.6 ; ; b = 57 ; ; c = 58.6 ; ;

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

p = a+b+c = 13.6+57+58.6 = 129.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 129.2 }{ 2 } = 64.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.6 * (64.6-13.6)(64.6-57)(64.6-58.6) } ; ; T = sqrt{ 150233.76 } = 387.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 387.6 }{ 13.6 } = 57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 387.6 }{ 57 } = 13.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 387.6 }{ 58.6 } = 13.23 ; ;

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{ 13.6**2-57**2-58.6**2 }{ 2 * 57 * 58.6 } ) = 13° 25'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 57**2-13.6**2-58.6**2 }{ 2 * 13.6 * 58.6 } ) = 76° 34'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 58.6**2-13.6**2-57**2 }{ 2 * 57 * 13.6 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 387.6 }{ 64.6 } = 6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.6 }{ 2 * sin 13° 25'11" } = 29.3 ; ;




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