8 14 15 triangle

Acute scalene triangle.

Sides: a = 8   b = 14   c = 15

Area: T = 55.31221822025
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ B = β = 67.20109687281° = 67°12'3″ = 1.17328781648 rad
Angle ∠ C = γ = 81.01107006548° = 81°39″ = 1.41439034558 rad

Height: ha = 13.82880455506
Height: hb = 7.90217403146
Height: hc = 7.3754957627

Median: ma = 13.9466325681
Median: mb = 9.77224101428
Median: mc = 8.58877820187

Inradius: r = 2.99898476866
Circumradius: R = 7.5933263966

Vertex coordinates: A[15; 0] B[0; 0] C[3.1; 7.3754957627]
Centroid: CG[6.03333333333; 2.4588319209]
Coordinates of the circumscribed circle: U[7.5; 1.18664474947]
Coordinates of the inscribed circle: I[4.5; 2.99898476866]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ B' = β' = 112.7999031272° = 112°47'57″ = 1.17328781648 rad
∠ C' = γ' = 98.98992993452° = 98°59'21″ = 1.41439034558 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 = 8 ; ; b = 14 ; ; c = 15 ; ;

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

p = a+b+c = 8+14+15 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-8)(18.5-14)(18.5-15) } ; ; T = sqrt{ 3059.44 } = 55.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.31 }{ 8 } = 13.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.31 }{ 14 } = 7.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.31 }{ 15 } = 7.37 ; ;

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{ 8**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 31° 47'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-8**2-15**2 }{ 2 * 8 * 15 } ) = 67° 12'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-8**2-14**2 }{ 2 * 14 * 8 } ) = 81° 39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.31 }{ 18.5 } = 2.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 31° 47'18" } = 7.59 ; ;




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