6960 5535 8895 triangle

Obtuse scalene triangle.

Sides: a = 6960   b = 5535   c = 8895

Area: T = 19261796.97222
Perimeter: p = 21390
Semiperimeter: s = 10695

Angle ∠ A = α = 51.48765437762° = 51°29'12″ = 0.89986097094 rad
Angle ∠ B = β = 38.481133075° = 38°28'53″ = 0.67216259221 rad
Angle ∠ C = γ = 90.03221254738° = 90°1'56″ = 1.57113570221 rad

Height: ha = 5534.999912996
Height: hb = 6959.999890596
Height: hc = 4330.927680658

Median: ma = 6539.742196739
Median: mb = 7491.47989094
Median: mc = 4445.071100618

Inradius: r = 1801.010953457
Circumradius: R = 4447.50106991

Vertex coordinates: A[8895; 0] B[0; 0] C[5448.364424958; 4330.927680658]
Centroid: CG[4781.121141653; 1443.642226886]
Coordinates of the circumscribed circle: U[4447.5; -2.49436925703]
Coordinates of the inscribed circle: I[5160; 1801.010953457]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.5133456224° = 128°30'48″ = 0.89986097094 rad
∠ B' = β' = 141.519866925° = 141°31'7″ = 0.67216259221 rad
∠ C' = γ' = 89.96878745262° = 89°58'4″ = 1.57113570221 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 = 6960 ; ; b = 5535 ; ; c = 8895 ; ;

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

p = a+b+c = 6960+5535+8895 = 21390 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21390 }{ 2 } = 10695 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10695 * (10695-6960)(10695-5535)(10695-8895) } ; ; T = sqrt{ 3.71 * 10**{ 14 } } = 19261796.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19261796.97 }{ 6960 } = 5535 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19261796.97 }{ 5535 } = 6960 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19261796.97 }{ 8895 } = 4330.93 ; ;

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{ 6960**2-5535**2-8895**2 }{ 2 * 5535 * 8895 } ) = 51° 29'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5535**2-6960**2-8895**2 }{ 2 * 6960 * 8895 } ) = 38° 28'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8895**2-6960**2-5535**2 }{ 2 * 5535 * 6960 } ) = 90° 1'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19261796.97 }{ 10695 } = 1801.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6960 }{ 2 * sin 51° 29'12" } = 4447.5 ; ;




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

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