7 25 28 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 25   c = 28

Area: T = 83.06662386292
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 13.72991326754° = 13°43'45″ = 0.24396185686 rad
Angle ∠ B = β = 57.95331689134° = 57°57'11″ = 1.01114736095 rad
Angle ∠ C = γ = 108.3187698411° = 108°19'4″ = 1.89105004755 rad

Height: ha = 23.73332110369
Height: hb = 6.64552990903
Height: hc = 5.93333027592

Median: ma = 26.31106442338
Median: mb = 16.13222658049
Median: mc = 11.8744342087

Inradius: r = 2.7698874621
Circumradius: R = 14.7477267003

Vertex coordinates: A[28; 0] B[0; 0] C[3.71442857143; 5.93333027592]
Centroid: CG[10.57114285714; 1.97877675864]
Coordinates of the circumscribed circle: U[14; -4.63548553438]
Coordinates of the inscribed circle: I[5; 2.7698874621]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.2710867325° = 166°16'15″ = 0.24396185686 rad
∠ B' = β' = 122.0476831087° = 122°2'49″ = 1.01114736095 rad
∠ C' = γ' = 71.68223015888° = 71°40'56″ = 1.89105004755 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 = 25 ; ; c = 28 ; ;

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

p = a+b+c = 7+25+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-7)(30-25)(30-28) } ; ; T = sqrt{ 6900 } = 83.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.07 }{ 7 } = 23.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.07 }{ 25 } = 6.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.07 }{ 28 } = 5.93 ; ;

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**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 13° 43'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-7**2-28**2 }{ 2 * 7 * 28 } ) = 57° 57'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-7**2-25**2 }{ 2 * 25 * 7 } ) = 108° 19'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.07 }{ 30 } = 2.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 43'45" } = 14.75 ; ;




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