8 17 21 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 17   c = 21

Area: T = 64.34328317686
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 21.12986972543° = 21°7'43″ = 0.36987653337 rad
Angle ∠ B = β = 49.99547991151° = 49°59'41″ = 0.87325738534 rad
Angle ∠ C = γ = 108.8776503631° = 108°52'35″ = 1.99002534664 rad

Height: ha = 16.08657079421
Height: hb = 7.5769744914
Height: hc = 6.12878887399

Median: ma = 18.68215416923
Median: mb = 13.42657215821
Median: mc = 8.1399410298

Inradius: r = 2.79875144247
Circumradius: R = 11.09768072181

Vertex coordinates: A[21; 0] B[0; 0] C[5.14328571429; 6.12878887399]
Centroid: CG[8.71442857143; 2.043262958]
Coordinates of the circumscribed circle: U[10.5; -3.59901435117]
Coordinates of the inscribed circle: I[6; 2.79875144247]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8711302746° = 158°52'17″ = 0.36987653337 rad
∠ B' = β' = 130.0055200885° = 130°19″ = 0.87325738534 rad
∠ C' = γ' = 71.12334963694° = 71°7'25″ = 1.99002534664 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 = 8 ; ; b = 17 ; ; c = 21 ; ;

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

p = a+b+c = 8+17+21 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-8)(23-17)(23-21) } ; ; T = sqrt{ 4140 } = 64.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.34 }{ 8 } = 16.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.34 }{ 17 } = 7.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.34 }{ 21 } = 6.13 ; ;

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{ 8**2-17**2-21**2 }{ 2 * 17 * 21 } ) = 21° 7'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-21**2 }{ 2 * 8 * 21 } ) = 49° 59'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 108° 52'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.34 }{ 23 } = 2.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 21° 7'43" } = 11.1 ; ;




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