22 24 28 triangle

Acute scalene triangle.

Sides: a = 22   b = 24   c = 28

Area: T = 254.8233468307
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 49.32436272308° = 49°19'25″ = 0.86108596942 rad
Angle ∠ B = β = 55.82773636603° = 55°49'38″ = 0.97443713086 rad
Angle ∠ C = γ = 74.84990091089° = 74°50'56″ = 1.30663616508 rad

Height: ha = 23.16657698461
Height: hb = 21.23552890256
Height: hc = 18.20216763076

Median: ma = 23.64331808351
Median: mb = 22.13659436212
Median: mc = 18.27656668825

Inradius: r = 6.88771207651
Circumradius: R = 14.50441586026

Vertex coordinates: A[28; 0] B[0; 0] C[12.35771428571; 18.20216763076]
Centroid: CG[13.45223809524; 6.06772254359]
Coordinates of the circumscribed circle: U[14; 3.79108596348]
Coordinates of the inscribed circle: I[13; 6.88771207651]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.6766372769° = 130°40'35″ = 0.86108596942 rad
∠ B' = β' = 124.173263634° = 124°10'22″ = 0.97443713086 rad
∠ C' = γ' = 105.1510990891° = 105°9'4″ = 1.30663616508 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 = 22 ; ; b = 24 ; ; c = 28 ; ;

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

p = a+b+c = 22+24+28 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-22)(37-24)(37-28) } ; ; T = sqrt{ 64935 } = 254.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 254.82 }{ 22 } = 23.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 254.82 }{ 24 } = 21.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 254.82 }{ 28 } = 18.2 ; ;

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{ 22**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 49° 19'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 55° 49'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-22**2-24**2 }{ 2 * 24 * 22 } ) = 74° 50'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 254.82 }{ 37 } = 6.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 49° 19'25" } = 14.5 ; ;




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