15 26 30 triangle

Acute scalene triangle.

Sides: a = 15   b = 26   c = 30

Area: T = 1954.999839743
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 309.9999728141° = 30° = 0.52435983011 rad
Angle ∠ B = β = 60.07334833336° = 60°4'25″ = 1.04884800773 rad
Angle ∠ C = γ = 89.92765438523° = 89°55'36″ = 1.57695142752 rad

Height: ha = 265.9999786325
Height: hb = 154.9999876726
Height: hc = 132.9999893162

Median: ma = 27.05108779894
Median: mb = 19.83768344249
Median: mc = 15.01766574177

Inradius: r = 5.49329532322
Circumradius: R = 155.0000123274

Vertex coordinates: A[30; 0] B[0; 0] C[7.48333333333; 132.9999893162]
Centroid: CG[12.49444444444; 4.33333297721]
Coordinates of the circumscribed circle: U[15; 0.0199230785]
Coordinates of the inscribed circle: I[9.5; 5.49329532322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1500.000027186° = 150° = 0.52435983011 rad
∠ B' = β' = 119.9276516666° = 119°55'35″ = 1.04884800773 rad
∠ C' = γ' = 90.07334561477° = 90°4'24″ = 1.57695142752 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 = 26 ; ; c = 30 ; ;

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

p = a+b+c = 15+26+30 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-15)(35.5-26)(35.5-30) } ; ; T = sqrt{ 38024.94 } = 195 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 195 }{ 15 } = 26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 195 }{ 26 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 195 }{ 30 } = 13 ; ;

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**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 30° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 60° 4'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-26**2 }{ 2 * 26 * 15 } ) = 89° 55'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 195 }{ 35.5 } = 5.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 30° } = 15 ; ;




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