7 22 28 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 22   c = 28

Area: T = 44.6265525207
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 8.33107975597° = 8°19'51″ = 0.14553998467 rad
Angle ∠ B = β = 27.08882606768° = 27°5'18″ = 0.47327793374 rad
Angle ∠ C = γ = 144.5810941764° = 144°34'51″ = 2.52334134694 rad

Height: ha = 12.75501500591
Height: hb = 4.05768659279
Height: hc = 3.18875375148

Median: ma = 24.93549152796
Median: mb = 17.19901134377
Median: mc = 8.39664278119

Inradius: r = 1.5665807902
Circumradius: R = 24.1576578438

Vertex coordinates: A[28; 0] B[0; 0] C[6.23221428571; 3.18875375148]
Centroid: CG[11.41107142857; 1.06325125049]
Coordinates of the circumscribed circle: U[14; -19.6866042818]
Coordinates of the inscribed circle: I[6.5; 1.5665807902]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.669920244° = 171°40'9″ = 0.14553998467 rad
∠ B' = β' = 152.9121739323° = 152°54'42″ = 0.47327793374 rad
∠ C' = γ' = 35.41990582365° = 35°25'9″ = 2.52334134694 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 = 28 ; ;

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

p = a+b+c = 7+22+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-7)(28.5-22)(28.5-28) } ; ; T = sqrt{ 1991.44 } = 44.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.63 }{ 7 } = 12.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.63 }{ 22 } = 4.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.63 }{ 28 } = 3.19 ; ;

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**2-28**2 }{ 2 * 22 * 28 } ) = 8° 19'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-28**2 }{ 2 * 7 * 28 } ) = 27° 5'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 144° 34'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.63 }{ 28.5 } = 1.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 8° 19'51" } = 24.16 ; ;




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