7 7 12 triangle

Obtuse isosceles triangle.

Sides: a = 7   b = 7   c = 12

Area: T = 21.63333076528
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 31.00327191339° = 31°10″ = 0.5411099526 rad
Angle ∠ B = β = 31.00327191339° = 31°10″ = 0.5411099526 rad
Angle ∠ C = γ = 117.9954561732° = 117°59'40″ = 2.05993936017 rad

Height: ha = 6.18109450437
Height: hb = 6.18109450437
Height: hc = 3.60655512755

Median: ma = 9.17987798753
Median: mb = 9.17987798753
Median: mc = 3.60655512755

Inradius: r = 1.66441005887
Circumradius: R = 6.79550774038

Vertex coordinates: A[12; 0] B[0; 0] C[6; 3.60655512755]
Centroid: CG[6; 1.20218504252]
Coordinates of the circumscribed circle: U[6; -3.19895261283]
Coordinates of the inscribed circle: I[6; 1.66441005887]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.9977280866° = 148°59'50″ = 0.5411099526 rad
∠ B' = β' = 148.9977280866° = 148°59'50″ = 0.5411099526 rad
∠ C' = γ' = 62.00554382677° = 62°20″ = 2.05993936017 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 = 7 ; ; c = 12 ; ;

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

p = a+b+c = 7+7+12 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-7)(13-7)(13-12) } ; ; T = sqrt{ 468 } = 21.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.63 }{ 7 } = 6.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.63 }{ 7 } = 6.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.63 }{ 12 } = 3.61 ; ;

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**2-7**2-12**2 }{ 2 * 7 * 12 } ) = 31° 10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-7**2-12**2 }{ 2 * 7 * 12 } ) = 31° 10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 117° 59'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.63 }{ 13 } = 1.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 31° 10" } = 6.8 ; ;




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