17 25 28 triangle

Acute scalene triangle.

Sides: a = 17   b = 25   c = 28

Area: T = 210
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ C = γ = 81.203258929° = 81°12'9″ = 1.41772525443 rad

Height: ha = 24.70658823529
Height: hb = 16.8
Height: hc = 15

Median: ma = 25.14545819214
Median: mb = 19.5
Median: mc = 16.15554944214

Inradius: r = 6
Circumradius: R = 14.16766666667

Vertex coordinates: A[28; 0] B[0; 0] C[8; 15]
Centroid: CG[12; 5]
Coordinates of the circumscribed circle: U[14; 2.16766666667]
Coordinates of the inscribed circle: I[10; 6]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 118.0722486936° = 118°4'21″ = 1.08108390005 rad
∠ C' = γ' = 98.797741071° = 98°47'51″ = 1.41772525443 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 = 17 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 17+25+28 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-17)(35-25)(35-28) } ; ; T = sqrt{ 44100 } = 210 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 210 }{ 17 } = 24.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 210 }{ 25 } = 16.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 210 }{ 28 } = 15 ; ;

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{ 17**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 36° 52'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 61° 55'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-25**2 }{ 2 * 25 * 17 } ) = 81° 12'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 210 }{ 35 } = 6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 36° 52'12" } = 14.17 ; ;




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