7 12 17 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 12   c = 17

Area: T = 34.46773758792
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 19.75499227956° = 19°45' = 0.34547011798 rad
Angle ∠ B = β = 35.44001726253° = 35°24'1″ = 0.61878495681 rad
Angle ∠ C = γ = 124.8549904579° = 124°51' = 2.17990419057 rad

Height: ha = 9.84878216798
Height: hb = 5.74545626465
Height: hc = 4.05549853976

Median: ma = 14.2921605928
Median: mb = 11.53325625947
Median: mc = 4.92444289009

Inradius: r = 1.91548542155
Circumradius: R = 10.35876205294

Vertex coordinates: A[17; 0] B[0; 0] C[5.70658823529; 4.05549853976]
Centroid: CG[7.5698627451; 1.35216617992]
Coordinates of the circumscribed circle: U[8.5; -5.91986403025]
Coordinates of the inscribed circle: I[6; 1.91548542155]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.2550077204° = 160°15' = 0.34547011798 rad
∠ B' = β' = 144.6599827375° = 144°35'59″ = 0.61878495681 rad
∠ C' = γ' = 55.1550095421° = 55°9' = 2.17990419057 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 = 12 ; ; c = 17 ; ;

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

p = a+b+c = 7+12+17 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-7)(18-12)(18-17) } ; ; T = sqrt{ 1188 } = 34.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.47 }{ 7 } = 9.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.47 }{ 12 } = 5.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.47 }{ 17 } = 4.05 ; ;

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**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 19° 45' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-7**2-17**2 }{ 2 * 7 * 17 } ) = 35° 24'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-7**2-12**2 }{ 2 * 12 * 7 } ) = 124° 51' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.47 }{ 18 } = 1.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 19° 45' } = 10.36 ; ;




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