15 25 26 triangle

Acute scalene triangle.

Sides: a = 15   b = 25   c = 26

Area: T = 182.3844209843
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 34.13875931378° = 34°8'15″ = 0.5965813399 rad
Angle ∠ B = β = 69.27772556184° = 69°16'38″ = 1.20991162073 rad
Angle ∠ C = γ = 76.58551512438° = 76°35'7″ = 1.33766630473 rad

Height: ha = 24.31878946457
Height: hb = 14.59107367874
Height: hc = 14.03295546033

Median: ma = 24.37772434865
Median: mb = 17.15437167984
Median: mc = 16

Inradius: r = 5.52767942377
Circumradius: R = 13.36546438039

Vertex coordinates: A[26; 0] B[0; 0] C[5.30876923077; 14.03295546033]
Centroid: CG[10.43658974359; 4.67765182011]
Coordinates of the circumscribed circle: U[13; 3.10105973625]
Coordinates of the inscribed circle: I[8; 5.52767942377]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.8622406862° = 145°51'45″ = 0.5965813399 rad
∠ B' = β' = 110.7232744382° = 110°43'22″ = 1.20991162073 rad
∠ C' = γ' = 103.4154848756° = 103°24'53″ = 1.33766630473 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 = 25 ; ; c = 26 ; ;

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

p = a+b+c = 15+25+26 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-15)(33-25)(33-26) } ; ; T = sqrt{ 33264 } = 182.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 182.38 }{ 15 } = 24.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 182.38 }{ 25 } = 14.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 182.38 }{ 26 } = 14.03 ; ;

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**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 34° 8'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 69° 16'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-25**2 }{ 2 * 25 * 15 } ) = 76° 35'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 182.38 }{ 33 } = 5.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 34° 8'15" } = 13.36 ; ;




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