7 12 16 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 12   c = 16

Area: T = 38.93550420573
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 23.92770614889° = 23°55'37″ = 0.41876060033 rad
Angle ∠ B = β = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ C = γ = 112.0244312837° = 112°1'28″ = 1.95551931013 rad

Height: ha = 11.12442977306
Height: hb = 6.48991736762
Height: hc = 4.86768802572

Median: ma = 13.7022189606
Median: mb = 10.79435165725
Median: mc = 5.70108771255

Inradius: r = 2.22548595461
Circumradius: R = 8.63297582395

Vertex coordinates: A[16; 0] B[0; 0] C[5.031125; 4.86768802572]
Centroid: CG[7.01104166667; 1.62222934191]
Coordinates of the circumscribed circle: U[8; -3.23661593398]
Coordinates of the inscribed circle: I[5.5; 2.22548595461]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0732938511° = 156°4'23″ = 0.41876060033 rad
∠ B' = β' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ C' = γ' = 67.9765687163° = 67°58'32″ = 1.95551931013 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 = 12 ; ; c = 16 ; ;

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

p = a+b+c = 7+12+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-7)(17.5-12)(17.5-16) } ; ; T = sqrt{ 1515.94 } = 38.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.94 }{ 7 } = 11.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.94 }{ 12 } = 6.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.94 }{ 16 } = 4.87 ; ;

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**2-12**2-16**2 }{ 2 * 12 * 16 } ) = 23° 55'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 44° 2'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-12**2 }{ 2 * 12 * 7 } ) = 112° 1'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.94 }{ 17.5 } = 2.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 23° 55'37" } = 8.63 ; ;




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