8 18 21 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 18   c = 21

Area: T = 70.77703151046
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 21.99900832984° = 21°59'24″ = 0.38437993563 rad
Angle ∠ B = β = 57.40554616926° = 57°24'20″ = 1.00219143152 rad
Angle ∠ C = γ = 100.6044455009° = 100°36'16″ = 1.75658789821 rad

Height: ha = 17.69325787761
Height: hb = 7.8633368345
Height: hc = 6.744003001

Median: ma = 19.14441897191
Median: mb = 13.09658008537
Median: mc = 9.15215026089

Inradius: r = 3.01215027704
Circumradius: R = 10.68224450178

Vertex coordinates: A[21; 0] B[0; 0] C[4.31095238095; 6.744003001]
Centroid: CG[8.43765079365; 2.247667667]
Coordinates of the circumscribed circle: U[10.5; -1.96658666179]
Coordinates of the inscribed circle: I[5.5; 3.01215027704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.0109916702° = 158°36″ = 0.38437993563 rad
∠ B' = β' = 122.5954538307° = 122°35'40″ = 1.00219143152 rad
∠ C' = γ' = 79.3965544991° = 79°23'44″ = 1.75658789821 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 = 18 ; ; c = 21 ; ;

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

p = a+b+c = 8+18+21 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-8)(23.5-18)(23.5-21) } ; ; T = sqrt{ 5008.44 } = 70.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.77 }{ 8 } = 17.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.77 }{ 18 } = 7.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.77 }{ 21 } = 6.74 ; ;

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**2-18**2-21**2 }{ 2 * 18 * 21 } ) = 21° 59'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-8**2-21**2 }{ 2 * 8 * 21 } ) = 57° 24'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-8**2-18**2 }{ 2 * 18 * 8 } ) = 100° 36'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.77 }{ 23.5 } = 3.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 21° 59'24" } = 10.68 ; ;




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