6 7 7 triangle

Acute isosceles triangle.

Sides: a = 6   b = 7   c = 7

Area: T = 18.9743665961
Perimeter: p = 20
Semiperimeter: s = 10

Angle ∠ A = α = 50.75438670503° = 50°45'14″ = 0.88658220881 rad
Angle ∠ B = β = 64.62330664748° = 64°37'23″ = 1.12878852827 rad
Angle ∠ C = γ = 64.62330664748° = 64°37'23″ = 1.12878852827 rad

Height: ha = 6.32545553203
Height: hb = 5.42110474174
Height: hc = 5.42110474174

Median: ma = 6.32545553203
Median: mb = 5.5
Median: mc = 5.5

Inradius: r = 1.89773665961
Circumradius: R = 3.87437901337

Vertex coordinates: A[7; 0] B[0; 0] C[2.57114285714; 5.42110474174]
Centroid: CG[3.19904761905; 1.80770158058]
Coordinates of the circumscribed circle: U[3.5; 1.66601957716]
Coordinates of the inscribed circle: I[3; 1.89773665961]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.246613295° = 129°14'46″ = 0.88658220881 rad
∠ B' = β' = 115.3776933525° = 115°22'37″ = 1.12878852827 rad
∠ C' = γ' = 115.3776933525° = 115°22'37″ = 1.12878852827 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 = 6 ; ; b = 7 ; ; c = 7 ; ;

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

p = a+b+c = 6+7+7 = 20 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20 }{ 2 } = 10 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10 * (10-6)(10-7)(10-7) } ; ; T = sqrt{ 360 } = 18.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.97 }{ 6 } = 6.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.97 }{ 7 } = 5.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.97 }{ 7 } = 5.42 ; ;

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{ 6**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 50° 45'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-6**2-7**2 }{ 2 * 6 * 7 } ) = 64° 37'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-6**2-7**2 }{ 2 * 7 * 6 } ) = 64° 37'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.97 }{ 10 } = 1.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 50° 45'14" } = 3.87 ; ;




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