5 25 26 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 25   c = 26

Area: T = 62.16110810717
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 11.02766094668° = 11°1'36″ = 0.19224506405 rad
Angle ∠ B = β = 73.00438351829° = 73°14″ = 1.27441572905 rad
Angle ∠ C = γ = 95.97695553502° = 95°58'10″ = 1.67549847225 rad

Height: ha = 24.86444324287
Height: hb = 4.97328864857
Height: hc = 4.78216216209

Median: ma = 25.3822080293
Median: mb = 13.93773598648
Median: mc = 12.49899959968

Inradius: r = 2.22200386097
Circumradius: R = 13.07108794955

Vertex coordinates: A[26; 0] B[0; 0] C[1.46215384615; 4.78216216209]
Centroid: CG[9.15438461538; 1.59438738736]
Coordinates of the circumscribed circle: U[13; -1.35993714675]
Coordinates of the inscribed circle: I[3; 2.22200386097]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.9733390533° = 168°58'24″ = 0.19224506405 rad
∠ B' = β' = 106.9966164817° = 106°59'46″ = 1.27441572905 rad
∠ C' = γ' = 84.03304446498° = 84°1'50″ = 1.67549847225 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 = 5 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 5+25+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-5)(28-25)(28-26) } ; ; T = sqrt{ 3864 } = 62.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.16 }{ 5 } = 24.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.16 }{ 25 } = 4.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.16 }{ 26 } = 4.78 ; ;

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{ 5**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 11° 1'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-5**2-26**2 }{ 2 * 5 * 26 } ) = 73° 14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-5**2-25**2 }{ 2 * 25 * 5 } ) = 95° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.16 }{ 28 } = 2.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 1'36" } = 13.07 ; ;




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