7 11 15 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 11   c = 15

Area: T = 35.96109162842
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ B = β = 43.23332348092° = 43°14' = 0.75545622937 rad
Angle ∠ C = γ = 110.9254832428° = 110°55'29″ = 1.93660035481 rad

Height: ha = 10.27545475098
Height: hb = 6.53883484153
Height: hc = 4.79547888379

Median: ma = 12.67987223331
Median: mb = 10.33219891599
Median: mc = 5.36219026474

Inradius: r = 2.17994494718
Circumradius: R = 8.03295506855

Vertex coordinates: A[15; 0] B[0; 0] C[5.1; 4.79547888379]
Centroid: CG[6.7; 1.5988262946]
Coordinates of the circumscribed circle: U[7.5; -2.86876966734]
Coordinates of the inscribed circle: I[5.5; 2.17994494718]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ B' = β' = 136.7676765191° = 136°46' = 0.75545622937 rad
∠ C' = γ' = 69.07551675724° = 69°4'31″ = 1.93660035481 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 = 11 ; ; c = 15 ; ;

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

p = a+b+c = 7+11+15 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-7)(16.5-11)(16.5-15) } ; ; T = sqrt{ 1293.19 } = 35.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.96 }{ 7 } = 10.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.96 }{ 11 } = 6.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.96 }{ 15 } = 4.79 ; ;

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**2-11**2-15**2 }{ 2 * 11 * 15 } ) = 25° 50'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-7**2-15**2 }{ 2 * 7 * 15 } ) = 43° 14' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-7**2-11**2 }{ 2 * 11 * 7 } ) = 110° 55'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.96 }{ 16.5 } = 2.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 25° 50'31" } = 8.03 ; ;




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