36 43.5 55.5 triangle

Acute scalene triangle.

Sides: a = 36   b = 43.5   c = 55.5

Area: T = 782.5344344294
Perimeter: p = 135
Semiperimeter: s = 67.5

Angle ∠ A = α = 40.41107591034° = 40°24'39″ = 0.70553007996 rad
Angle ∠ B = β = 51.56553491823° = 51°33'55″ = 0.98999851232 rad
Angle ∠ C = γ = 88.02438917143° = 88°1'26″ = 1.53663067308 rad

Height: ha = 43.47441302386
Height: hb = 35.97985905423
Height: hc = 28.19994358304

Median: ma = 46.5
Median: mb = 41.41333130768
Median: mc = 28.70664888135

Inradius: r = 11.5933101397
Circumradius: R = 27.7676512944

Vertex coordinates: A[55.5; 0] B[0; 0] C[22.37883783784; 28.19994358304]
Centroid: CG[25.95994594595; 9.43998119435]
Coordinates of the circumscribed circle: U[27.75; 0.95774659636]
Coordinates of the inscribed circle: I[24; 11.5933101397]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.5899240897° = 139°35'21″ = 0.70553007996 rad
∠ B' = β' = 128.4354650818° = 128°26'5″ = 0.98999851232 rad
∠ C' = γ' = 91.97661082857° = 91°58'34″ = 1.53663067308 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 = 36 ; ; b = 43.5 ; ; c = 55.5 ; ;

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

p = a+b+c = 36+43.5+55.5 = 135 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 135 }{ 2 } = 67.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 67.5 * (67.5-36)(67.5-43.5)(67.5-55.5) } ; ; T = sqrt{ 612360 } = 782.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 782.53 }{ 36 } = 43.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 782.53 }{ 43.5 } = 35.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 782.53 }{ 55.5 } = 28.2 ; ;

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{ 43.5**2+55.5**2-36**2 }{ 2 * 43.5 * 55.5 } ) = 40° 24'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 36**2+55.5**2-43.5**2 }{ 2 * 36 * 55.5 } ) = 51° 33'55" ; ; gamma = 180° - alpha - beta = 180° - 40° 24'39" - 51° 33'55" = 88° 1'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 782.53 }{ 67.5 } = 11.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 36 }{ 2 * sin 40° 24'39" } = 27.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.5**2+2 * 55.5**2 - 36**2 } }{ 2 } = 46.5 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 55.5**2+2 * 36**2 - 43.5**2 } }{ 2 } = 41.413 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 43.5**2+2 * 36**2 - 55.5**2 } }{ 2 } = 28.706 ; ;
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.