10 17 21 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 17   c = 21

Area: T = 84
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 98.797741071° = 98°47'51″ = 1.72443401093 rad

Height: ha = 16.8
Height: hb = 9.88223529412
Height: hc = 8

Median: ma = 18.43990889146
Median: mb = 14.08801278403
Median: mc = 9.17987798753

Inradius: r = 3.5
Circumradius: R = 10.625

Vertex coordinates: A[21; 0] B[0; 0] C[6; 8]
Centroid: CG[9; 2.66766666667]
Coordinates of the circumscribed circle: U[10.5; -1.625]
Coordinates of the inscribed circle: I[7; 3.5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 81.203258929° = 81°12'9″ = 1.72443401093 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 = 10 ; ; b = 17 ; ; c = 21 ; ;

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

p = a+b+c = 10+17+21 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-10)(24-17)(24-21) } ; ; T = sqrt{ 7056 } = 84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84 }{ 10 } = 16.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84 }{ 17 } = 9.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84 }{ 21 } = 8 ; ;

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{ 17**2+21**2-10**2 }{ 2 * 17 * 21 } ) = 28° 4'21" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+21**2-17**2 }{ 2 * 10 * 21 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 10**2+17**2-21**2 }{ 2 * 10 * 17 } ) = 98° 47'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84 }{ 24 } = 3.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 28° 4'21" } = 10.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 21**2 - 10**2 } }{ 2 } = 18.439 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 10**2 - 17**2 } }{ 2 } = 14.08 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 10**2 - 21**2 } }{ 2 } = 9.179 ; ;
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.