7 14 15 triangle

Acute scalene triangle.

Sides: a = 7   b = 14   c = 15

Area: T = 48.74442304278
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 27.66604498993° = 27°39'38″ = 0.48327659233 rad
Angle ∠ B = β = 68.19662520106° = 68°11'47″ = 1.19902491351 rad
Angle ∠ C = γ = 84.14332980901° = 84°8'36″ = 1.46985775952 rad

Height: ha = 13.92769229794
Height: hb = 6.96334614897
Height: hc = 6.49992307237

Median: ma = 14.08801278403
Median: mb = 9.38108315196
Median: mc = 8.1399410298

Inradius: r = 2.70880128015
Circumradius: R = 7.53993538225

Vertex coordinates: A[15; 0] B[0; 0] C[2.6; 6.49992307237]
Centroid: CG[5.86766666667; 2.16664102412]
Coordinates of the circumscribed circle: U[7.5; 0.76993218186]
Coordinates of the inscribed circle: I[4; 2.70880128015]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.3439550101° = 152°20'22″ = 0.48327659233 rad
∠ B' = β' = 111.8043747989° = 111°48'13″ = 1.19902491351 rad
∠ C' = γ' = 95.85767019099° = 95°51'24″ = 1.46985775952 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 = 7 ; ; b = 14 ; ; c = 15 ; ;

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

p = a+b+c = 7+14+15 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-7)(18-14)(18-15) } ; ; T = sqrt{ 2376 } = 48.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.74 }{ 7 } = 13.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.74 }{ 14 } = 6.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.74 }{ 15 } = 6.5 ; ;

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{ 7**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 27° 39'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-15**2 }{ 2 * 7 * 15 } ) = 68° 11'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 84° 8'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.74 }{ 18 } = 2.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 27° 39'38" } = 7.54 ; ;




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