15 23 26 triangle

Acute scalene triangle.

Sides: a = 15   b = 23   c = 26

Area: T = 171.3944282285
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 34.9755424097° = 34°58'32″ = 0.61104363078 rad
Angle ∠ B = β = 61.51553646048° = 61°30'55″ = 1.07436456529 rad
Angle ∠ C = γ = 83.50992112982° = 83°30'33″ = 1.45875106929 rad

Height: ha = 22.85325709713
Height: hb = 14.90438506335
Height: hc = 13.18441755604

Median: ma = 23.3721991785
Median: mb = 17.84395627749
Median: mc = 14.42222051019

Inradius: r = 5.35660713214
Circumradius: R = 13.08438670351

Vertex coordinates: A[26; 0] B[0; 0] C[7.15438461538; 13.18441755604]
Centroid: CG[11.05112820513; 4.39547251868]
Coordinates of the circumscribed circle: U[13; 1.47990458388]
Coordinates of the inscribed circle: I[9; 5.35660713214]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0254575903° = 145°1'28″ = 0.61104363078 rad
∠ B' = β' = 118.4854635395° = 118°29'5″ = 1.07436456529 rad
∠ C' = γ' = 96.49107887018° = 96°29'27″ = 1.45875106929 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 15+23+26 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-15)(32-23)(32-26) } ; ; T = sqrt{ 29376 } = 171.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.39 }{ 15 } = 22.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.39 }{ 23 } = 14.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.39 }{ 26 } = 13.18 ; ;

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**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 34° 58'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 61° 30'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-23**2 }{ 2 * 23 * 15 } ) = 83° 30'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.39 }{ 32 } = 5.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 34° 58'32" } = 13.08 ; ;




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