9 18 26 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 18   c = 26

Area: T = 44.39552418622
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 10.93766341702° = 10°56'12″ = 0.19108802754 rad
Angle ∠ B = β = 22.29994025333° = 22°17'58″ = 0.38991979954 rad
Angle ∠ C = γ = 146.7643963296° = 146°45'50″ = 2.56215143828 rad

Height: ha = 9.86656093027
Height: hb = 4.93328046514
Height: hc = 3.41550186048

Median: ma = 21.90331961138
Median: mb = 17.24881883107
Median: mc = 5.78879184514

Inradius: r = 1.67552921457
Circumradius: R = 23.71987580432

Vertex coordinates: A[26; 0] B[0; 0] C[8.32769230769; 3.41550186048]
Centroid: CG[11.44223076923; 1.13883395349]
Coordinates of the circumscribed circle: U[13; -19.8398837746]
Coordinates of the inscribed circle: I[8.5; 1.67552921457]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.063336583° = 169°3'48″ = 0.19108802754 rad
∠ B' = β' = 157.7010597467° = 157°42'2″ = 0.38991979954 rad
∠ C' = γ' = 33.23660367035° = 33°14'10″ = 2.56215143828 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 = 9 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 9+18+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-9)(26.5-18)(26.5-26) } ; ; T = sqrt{ 1970.94 } = 44.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.4 }{ 9 } = 9.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.4 }{ 18 } = 4.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.4 }{ 26 } = 3.42 ; ;

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{ 9**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 10° 56'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 22° 17'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-18**2 }{ 2 * 18 * 9 } ) = 146° 45'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.4 }{ 26.5 } = 1.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 10° 56'12" } = 23.72 ; ;




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