17 18 26 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 18   c = 26

Area: T = 152.1877179158
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 40.57696972304° = 40°34'11″ = 0.70880747932 rad
Angle ∠ B = β = 43.52217409237° = 43°31'18″ = 0.76595976753 rad
Angle ∠ C = γ = 95.9098561846° = 95°54'31″ = 1.67439201851 rad

Height: ha = 17.90443740186
Height: hb = 16.91096865731
Height: hc = 11.70767060891

Median: ma = 20.68221178799
Median: mb = 20.03774649095
Median: mc = 11.72660393996

Inradius: r = 4.99897435789
Circumradius: R = 13.06994320705

Vertex coordinates: A[26; 0] B[0; 0] C[12.32769230769; 11.70767060891]
Centroid: CG[12.77656410256; 3.9022235363]
Coordinates of the circumscribed circle: U[13; -1.34553827131]
Coordinates of the inscribed circle: I[12.5; 4.99897435789]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.433030277° = 139°25'49″ = 0.70880747932 rad
∠ B' = β' = 136.4788259076° = 136°28'42″ = 0.76595976753 rad
∠ C' = γ' = 84.0911438154° = 84°5'29″ = 1.67439201851 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 = 18 ; ; c = 26 ; ;

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

p = a+b+c = 17+18+26 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-17)(30.5-18)(30.5-26) } ; ; T = sqrt{ 23160.94 } = 152.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 152.19 }{ 17 } = 17.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 152.19 }{ 18 } = 16.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 152.19 }{ 26 } = 11.71 ; ;

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**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 40° 34'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 43° 31'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 95° 54'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 152.19 }{ 30.5 } = 4.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 34'11" } = 13.07 ; ;




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