7 12 12 triangle

Acute isosceles triangle.

Sides: a = 7   b = 12   c = 12

Area: T = 40.17438409914
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 33.91655266° = 33°54'56″ = 0.59219376067 rad
Angle ∠ B = β = 73.04222367° = 73°2'32″ = 1.27548275234 rad
Angle ∠ C = γ = 73.04222367° = 73°2'32″ = 1.27548275234 rad

Height: ha = 11.47882402832
Height: hb = 6.69656401652
Height: hc = 6.69656401652

Median: ma = 11.47882402832
Median: mb = 7.77881745931
Median: mc = 7.77881745931

Inradius: r = 2.59218607091
Circumradius: R = 6.27327385229

Vertex coordinates: A[12; 0] B[0; 0] C[2.04216666667; 6.69656401652]
Centroid: CG[4.68105555556; 2.23218800551]
Coordinates of the circumscribed circle: U[6; 1.83295487358]
Coordinates of the inscribed circle: I[3.5; 2.59218607091]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.08444734° = 146°5'4″ = 0.59219376067 rad
∠ B' = β' = 106.95877633° = 106°57'28″ = 1.27548275234 rad
∠ C' = γ' = 106.95877633° = 106°57'28″ = 1.27548275234 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 = 12 ; ;

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

p = a+b+c = 7+12+12 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-7)(15.5-12)(15.5-12) } ; ; T = sqrt{ 1613.94 } = 40.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.17 }{ 7 } = 11.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.17 }{ 12 } = 6.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.17 }{ 12 } = 6.7 ; ;

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**2-12**2 }{ 2 * 12 * 12 } ) = 33° 54'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-7**2-12**2 }{ 2 * 7 * 12 } ) = 73° 2'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-7**2-12**2 }{ 2 * 12 * 7 } ) = 73° 2'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.17 }{ 15.5 } = 2.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 33° 54'56" } = 6.27 ; ;




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