15 21 26 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 21   c = 26

Area: T = 157.488015748
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 35.22993196511° = 35°13'46″ = 0.61548676211 rad
Angle ∠ B = β = 53.86111853369° = 53°51'40″ = 0.94400550232 rad
Angle ∠ C = γ = 90.9099495012° = 90°54'34″ = 1.58766700093 rad

Height: ha = 20.99773543307
Height: hb = 14.99881102362
Height: hc = 12.11438582677

Median: ma = 22.4110934831
Median: mb = 18.44658667457
Median: mc = 12.80662484749

Inradius: r = 5.088000508
Circumradius: R = 13.00216380016

Vertex coordinates: A[26; 0] B[0; 0] C[8.84661538462; 12.11438582677]
Centroid: CG[11.61553846154; 4.03879527559]
Coordinates of the circumscribed circle: U[13; -0.20663752064]
Coordinates of the inscribed circle: I[10; 5.088000508]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.7710680349° = 144°46'14″ = 0.61548676211 rad
∠ B' = β' = 126.1398814663° = 126°8'20″ = 0.94400550232 rad
∠ C' = γ' = 89.0910504988° = 89°5'26″ = 1.58766700093 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 = 21 ; ; c = 26 ; ;

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

p = a+b+c = 15+21+26 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-15)(31-21)(31-26) } ; ; T = sqrt{ 24800 } = 157.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 157.48 }{ 15 } = 21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 157.48 }{ 21 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 157.48 }{ 26 } = 12.11 ; ;

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**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 35° 13'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 53° 51'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-21**2 }{ 2 * 21 * 15 } ) = 90° 54'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 157.48 }{ 31 } = 5.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 35° 13'46" } = 13 ; ;




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