22 25 30 triangle

Acute scalene triangle.

Sides: a = 22   b = 25   c = 30

Area: T = 269.9910624837
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 46.05224163943° = 46°3'9″ = 0.80437662946 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 79.04772158011° = 79°2'50″ = 1.38796341803 rad

Height: ha = 24.54546022579
Height: hb = 21.5999249987
Height: hc = 17.99993749891

Median: ma = 25.32878502838
Median: mb = 23.14662739982
Median: mc = 18.15221348607

Inradius: r = 7.01327435023
Circumradius: R = 15.27883082838

Vertex coordinates: A[30; 0] B[0; 0] C[12.65; 17.99993749891]
Centroid: CG[14.21766666667; 65.999791663]
Coordinates of the circumscribed circle: U[15; 2.90328785739]
Coordinates of the inscribed circle: I[13.5; 7.01327435023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.9487583606° = 133°56'51″ = 0.80437662946 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 100.9532784199° = 100°57'10″ = 1.38796341803 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 22+25+30 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-22)(38.5-25)(38.5-30) } ; ; T = sqrt{ 72894.94 } = 269.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 269.99 }{ 22 } = 24.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 269.99 }{ 25 } = 21.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 269.99 }{ 30 } = 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{ 22**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 46° 3'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 54° 54'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-22**2-25**2 }{ 2 * 25 * 22 } ) = 79° 2'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 269.99 }{ 38.5 } = 7.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 46° 3'9" } = 15.28 ; ;




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