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?

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 = 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 57**2+58.6**2-13.6**2 }{ 2 * 57 * 58.6 } ) = 13° 25'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.6**2+58.6**2-57**2 }{ 2 * 13.6 * 58.6 } ) = 76° 34'49" ; ; gamma = 180° - alpha - beta = 180° - 13° 25'11" - 76° 34'49" = 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 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 57**2+2 * 58.6**2 - 13.6**2 } }{ 2 } = 57.404 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 58.6**2+2 * 13.6**2 - 57**2 } }{ 2 } = 31.579 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 57**2+2 * 13.6**2 - 58.6**2 } }{ 2 } = 29.3 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.