7 22 25 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 22   c = 25

Area: T = 73.48546922835
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 15.49987327566° = 15°29'55″ = 0.27105039165 rad
Angle ∠ B = β = 57.12216504356° = 57°7'18″ = 0.99769608743 rad
Angle ∠ C = γ = 107.3879616808° = 107°22'47″ = 1.87441278628 rad

Height: ha = 20.99656263667
Height: hb = 6.68804265712
Height: hc = 5.87987753827

Median: ma = 23.28662620444
Median: mb = 14.69769384567
Median: mc = 10.5

Inradius: r = 2.72216552698
Circumradius: R = 13.09879659857

Vertex coordinates: A[25; 0] B[0; 0] C[3.8; 5.87987753827]
Centroid: CG[9.6; 1.96595917942]
Coordinates of the circumscribed circle: U[12.5; -3.91223794503]
Coordinates of the inscribed circle: I[5; 2.72216552698]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.5011267243° = 164°30'5″ = 0.27105039165 rad
∠ B' = β' = 122.8788349564° = 122°52'42″ = 0.99769608743 rad
∠ C' = γ' = 72.62203831922° = 72°37'13″ = 1.87441278628 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 = 22 ; ; c = 25 ; ;

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

p = a+b+c = 7+22+25 = 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 * (27-7)(27-22)(27-25) } ; ; T = sqrt{ 5400 } = 73.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.48 }{ 7 } = 21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.48 }{ 22 } = 6.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.48 }{ 25 } = 5.88 ; ;

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**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 15° 29'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 57° 7'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 107° 22'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.48 }{ 27 } = 2.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 29'55" } = 13.1 ; ;




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