10 20 24 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 20   c = 24

Area: T = 98.17884090317
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 24.14768479965° = 24°8'49″ = 0.42114420015 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 100.9532784199° = 100°57'10″ = 1.76219584733 rad

Height: ha = 19.63656818063
Height: hb = 9.81878409032
Height: hc = 8.1821534086

Median: ma = 21.51774347914
Median: mb = 15.42772486205
Median: mc = 10.2965630141

Inradius: r = 3.63662373715
Circumradius: R = 12.2232646627

Vertex coordinates: A[24; 0] B[0; 0] C[5.75; 8.1821534086]
Centroid: CG[9.91766666667; 2.72771780287]
Coordinates of the circumscribed circle: U[12; -2.32223028591]
Coordinates of the inscribed circle: I[7; 3.63662373715]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.8533152003° = 155°51'11″ = 0.42114420015 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 79.04772158011° = 79°2'50″ = 1.76219584733 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 = 10 ; ; b = 20 ; ; c = 24 ; ;

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

p = a+b+c = 10+20+24 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-10)(27-20)(27-24) } ; ; T = sqrt{ 9639 } = 98.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.18 }{ 10 } = 19.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.18 }{ 20 } = 9.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.18 }{ 24 } = 8.18 ; ;

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{ 10**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 24° 8'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-10**2-24**2 }{ 2 * 10 * 24 } ) = 54° 54'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-10**2-20**2 }{ 2 * 20 * 10 } ) = 100° 57'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.18 }{ 27 } = 3.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 24° 8'49" } = 12.22 ; ;




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