12 15 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 15   c = 26

Area: T = 47.00546540249
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 13.9488491432° = 13°56'55″ = 0.24334471012 rad
Angle ∠ B = β = 17.53664150077° = 17°32'11″ = 0.30660681809 rad
Angle ∠ C = γ = 148.515509356° = 148°30'54″ = 2.59220773715 rad

Height: ha = 7.83441090041
Height: hb = 6.26772872033
Height: hc = 3.61657426173

Median: ma = 20.35992730715
Median: mb = 18.80882428738
Median: mc = 3.9377003937

Inradius: r = 1.77437605292
Circumradius: R = 24.89111522544

Vertex coordinates: A[26; 0] B[0; 0] C[11.44223076923; 3.61657426173]
Centroid: CG[12.48107692308; 1.20552475391]
Coordinates of the circumscribed circle: U[13; -21.22766215059]
Coordinates of the inscribed circle: I[11.5; 1.77437605292]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.0521508568° = 166°3'5″ = 0.24334471012 rad
∠ B' = β' = 162.4643584992° = 162°27'49″ = 0.30660681809 rad
∠ C' = γ' = 31.48549064397° = 31°29'6″ = 2.59220773715 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 = 12 ; ; b = 15 ; ; c = 26 ; ;

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

p = a+b+c = 12+15+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 * (26.5-12)(26.5-15)(26.5-26) } ; ; T = sqrt{ 2209.44 } = 47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47 }{ 12 } = 7.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47 }{ 15 } = 6.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47 }{ 26 } = 3.62 ; ;

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{ 12**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 13° 56'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 17° 32'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-15**2 }{ 2 * 15 * 12 } ) = 148° 30'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47 }{ 26.5 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 13° 56'55" } = 24.89 ; ;




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