7 10 16 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 10   c = 16

Area: T = 22.57107221861
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 16.38876115035° = 16°23'15″ = 0.28660177773 rad
Angle ∠ B = β = 23.76989007051° = 23°46'8″ = 0.41548455769 rad
Angle ∠ C = γ = 139.8433487791° = 139°50'37″ = 2.44107292994 rad

Height: ha = 6.44987777674
Height: hb = 4.51441444372
Height: hc = 2.82113402733

Median: ma = 12.87443931896
Median: mb = 11.29215897906
Median: mc = 3.24403703492

Inradius: r = 1.36879225567
Circumradius: R = 12.40554515266

Vertex coordinates: A[16; 0] B[0; 0] C[6.406625; 2.82113402733]
Centroid: CG[7.469875; 0.94404467578]
Coordinates of the circumscribed circle: U[8; -9.48113093811]
Coordinates of the inscribed circle: I[6.5; 1.36879225567]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.6122388497° = 163°36'45″ = 0.28660177773 rad
∠ B' = β' = 156.2311099295° = 156°13'52″ = 0.41548455769 rad
∠ C' = γ' = 40.15765122086° = 40°9'23″ = 2.44107292994 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 = 10 ; ; c = 16 ; ;

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

p = a+b+c = 7+10+16 = 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)(16.5-10)(16.5-16) } ; ; T = sqrt{ 509.44 } = 22.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.57 }{ 7 } = 6.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.57 }{ 10 } = 4.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.57 }{ 16 } = 2.82 ; ;

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**2-10**2-16**2 }{ 2 * 10 * 16 } ) = 16° 23'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 23° 46'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-10**2 }{ 2 * 10 * 7 } ) = 139° 50'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.57 }{ 16.5 } = 1.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 23'15" } = 12.41 ; ;




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