7 13 16 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 13   c = 16

Area: T = 44.49771909226
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 25.33216750167° = 25°19'54″ = 0.44221211341 rad
Angle ∠ B = β = 52.61768015821° = 52°37' = 0.91883364295 rad
Angle ∠ C = γ = 102.0521523401° = 102°3'5″ = 1.781113509 rad

Height: ha = 12.71334831207
Height: hb = 6.84657216804
Height: hc = 5.56221488653

Median: ma = 14.15109716981
Median: mb = 10.5
Median: mc = 6.70882039325

Inradius: r = 2.47220661624
Circumradius: R = 8.18802916646

Vertex coordinates: A[16; 0] B[0; 0] C[4.25; 5.56221488653]
Centroid: CG[6.75; 1.85440496218]
Coordinates of the circumscribed circle: U[8; -1.70879729849]
Coordinates of the inscribed circle: I[5; 2.47220661624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6688324983° = 154°40'6″ = 0.44221211341 rad
∠ B' = β' = 127.3833198418° = 127°23' = 0.91883364295 rad
∠ C' = γ' = 77.94884765988° = 77°56'55″ = 1.781113509 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 = 13 ; ; c = 16 ; ;

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

p = a+b+c = 7+13+16 = 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)(18-13)(18-16) } ; ; T = sqrt{ 1980 } = 44.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.5 }{ 7 } = 12.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.5 }{ 13 } = 6.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.5 }{ 16 } = 5.56 ; ;

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**2-13**2-16**2 }{ 2 * 13 * 16 } ) = 25° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 52° 37' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-13**2 }{ 2 * 13 * 7 } ) = 102° 3'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.5 }{ 18 } = 2.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 25° 19'54" } = 8.18 ; ;




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