7 15 16 triangle

Acute scalene triangle.

Sides: a = 7   b = 15   c = 16

Area: T = 52.30767873225
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 25.84219327632° = 25°50'31″ = 0.45110268118 rad
Angle ∠ B = β = 69.07551675724° = 69°4'31″ = 1.20655891055 rad
Angle ∠ C = γ = 85.08328996645° = 85°4'58″ = 1.48549767363 rad

Height: ha = 14.94547963779
Height: hb = 6.97442383097
Height: hc = 6.53883484153

Median: ma = 15.10879449297
Median: mb = 9.81107084352
Median: mc = 8.54440037453

Inradius: r = 2.75329888064
Circumradius: R = 8.03295506855

Vertex coordinates: A[16; 0] B[0; 0] C[2.5; 6.53883484153]
Centroid: CG[6.16766666667; 2.17994494718]
Coordinates of the circumscribed circle: U[8; 0.68882472016]
Coordinates of the inscribed circle: I[4; 2.75329888064]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1588067237° = 154°9'29″ = 0.45110268118 rad
∠ B' = β' = 110.9254832428° = 110°55'29″ = 1.20655891055 rad
∠ C' = γ' = 94.91771003355° = 94°55'2″ = 1.48549767363 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 = 15 ; ; c = 16 ; ;

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

p = a+b+c = 7+15+16 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-7)(19-15)(19-16) } ; ; T = sqrt{ 2736 } = 52.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.31 }{ 7 } = 14.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.31 }{ 15 } = 6.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.31 }{ 16 } = 6.54 ; ;

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**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 25° 50'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 69° 4'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-15**2 }{ 2 * 15 * 7 } ) = 85° 4'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.31 }{ 19 } = 2.75 ; ;

7. Circumradius

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




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