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' = 149.49897625939° = 149°29'23″ = 0.53325040983 rad
∠ B' = β' = 120.51102374061° = 120°30'37″ = 1.03882922285 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 = 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 56**2+65**2-33**2 }{ 2 * 56 * 65 } ) = 30° 30'37" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 33**2+65**2-56**2 }{ 2 * 33 * 65 } ) = 59° 29'23" ; ; gamma = 180° - alpha - beta = 180° - 30° 30'37" - 59° 29'23" = 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 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 56**2+2 * 65**2 - 33**2 } }{ 2 } = 58.38 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 65**2+2 * 33**2 - 56**2 } }{ 2 } = 43.278 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 56**2+2 * 33**2 - 65**2 } }{ 2 } = 32.5 ; ;
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.