15 20 26 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 20   c = 26

Area: T = 149.4577142686
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 35.08880894599° = 35°5'17″ = 0.61224026893 rad
Angle ∠ B = β = 50.03658856705° = 50°2'9″ = 0.87332909491 rad
Angle ∠ C = γ = 94.87660248696° = 94°52'34″ = 1.65658990152 rad

Height: ha = 19.92876190249
Height: hb = 14.94657142686
Height: hc = 11.49767032836

Median: ma = 21.94988040676
Median: mb = 18.72216452268
Median: mc = 11.97991485507

Inradius: r = 4.99002341864
Circumradius: R = 13.047721852

Vertex coordinates: A[26; 0] B[0; 0] C[9.63546153846; 11.49767032836]
Centroid: CG[11.87882051282; 3.83222344279]
Coordinates of the circumscribed circle: U[13; -1.10990135742]
Coordinates of the inscribed circle: I[10.5; 4.99002341864]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.912191054° = 144°54'43″ = 0.61224026893 rad
∠ B' = β' = 129.964411433° = 129°57'51″ = 0.87332909491 rad
∠ C' = γ' = 85.12439751304° = 85°7'26″ = 1.65658990152 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 = 15 ; ; b = 20 ; ; c = 26 ; ;

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

p = a+b+c = 15+20+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 * (30.5-15)(30.5-20)(30.5-26) } ; ; T = sqrt{ 22337.44 } = 149.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 149.46 }{ 15 } = 19.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 149.46 }{ 20 } = 14.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 149.46 }{ 26 } = 11.5 ; ;

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{ 15**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 35° 5'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 50° 2'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-20**2 }{ 2 * 20 * 15 } ) = 94° 52'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 149.46 }{ 30.5 } = 4.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 35° 5'17" } = 13.05 ; ;




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