7 18 21 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 18   c = 21

Area: T = 60.66330035524
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 18.721149202° = 18°43'17″ = 0.32767516766 rad
Angle ∠ B = β = 55.62436862764° = 55°37'25″ = 0.97108164676 rad
Angle ∠ C = γ = 105.6554821704° = 105°39'17″ = 1.84440245093 rad

Height: ha = 17.33222867293
Height: hb = 6.7440333728
Height: hc = 5.77774289098

Median: ma = 19.24218814049
Median: mb = 12.80662484749
Median: mc = 8.73221245983

Inradius: r = 2.63875218936
Circumradius: R = 10.90545045788

Vertex coordinates: A[21; 0] B[0; 0] C[3.95223809524; 5.77774289098]
Centroid: CG[8.31774603175; 1.92658096366]
Coordinates of the circumscribed circle: U[10.5; -2.94224853625]
Coordinates of the inscribed circle: I[5; 2.63875218936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.279850798° = 161°16'43″ = 0.32767516766 rad
∠ B' = β' = 124.3766313724° = 124°22'35″ = 0.97108164676 rad
∠ C' = γ' = 74.34551782964° = 74°20'43″ = 1.84440245093 rad

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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 = 7 ; ; b = 18 ; ; c = 21 ; ;

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

p = a+b+c = 7+18+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 * (23-7)(23-18)(23-21) } ; ; T = sqrt{ 3680 } = 60.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60.66 }{ 7 } = 17.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60.66 }{ 18 } = 6.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60.66 }{ 21 } = 5.78 ; ;

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{ 7**2-18**2-21**2 }{ 2 * 18 * 21 } ) = 18° 43'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-7**2-21**2 }{ 2 * 7 * 21 } ) = 55° 37'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-7**2-18**2 }{ 2 * 18 * 7 } ) = 105° 39'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60.66 }{ 23 } = 2.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 18° 43'17" } = 10.9 ; ;




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