3 7 7 triangle

Acute isosceles triangle.

Sides: a = 3   b = 7   c = 7

Area: T = 10.25660957484
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 24.74772502324° = 24°44'50″ = 0.43219209974 rad
Angle ∠ B = β = 77.62663748838° = 77°37'35″ = 1.35548358281 rad
Angle ∠ C = γ = 77.62663748838° = 77°37'35″ = 1.35548358281 rad

Height: ha = 6.83773971656
Height: hb = 2.9330313071
Height: hc = 2.9330313071

Median: ma = 6.83773971656
Median: mb = 4.09326763859
Median: mc = 4.09326763859

Inradius: r = 1.20765994998
Circumradius: R = 3.58332348782

Vertex coordinates: A[7; 0] B[0; 0] C[0.64328571429; 2.9330313071]
Centroid: CG[2.54876190476; 0.97767710237]
Coordinates of the circumscribed circle: U[3.5; 0.76878360453]
Coordinates of the inscribed circle: I[1.5; 1.20765994998]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.2532749768° = 155°15'10″ = 0.43219209974 rad
∠ B' = β' = 102.3743625116° = 102°22'25″ = 1.35548358281 rad
∠ C' = γ' = 102.3743625116° = 102°22'25″ = 1.35548358281 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 = 3 ; ; b = 7 ; ; c = 7 ; ;

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

p = a+b+c = 3+7+7 = 17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17 }{ 2 } = 8.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.5 * (8.5-3)(8.5-7)(8.5-7) } ; ; T = sqrt{ 105.19 } = 10.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.26 }{ 3 } = 6.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.26 }{ 7 } = 2.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.26 }{ 7 } = 2.93 ; ;

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{ 3**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 24° 44'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-3**2-7**2 }{ 2 * 3 * 7 } ) = 77° 37'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-3**2-7**2 }{ 2 * 7 * 3 } ) = 77° 37'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.26 }{ 8.5 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 24° 44'50" } = 3.58 ; ;




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