7 9 9 triangle

Acute isosceles triangle.

Sides: a = 7   b = 9   c = 9

Area: T = 29.02204669156
Perimeter: p = 25
Semiperimeter: s = 12.5

Angle ∠ A = α = 45.77107609523° = 45°46'15″ = 0.79988504798 rad
Angle ∠ B = β = 67.11546195238° = 67°6'53″ = 1.17113710869 rad
Angle ∠ C = γ = 67.11546195238° = 67°6'53″ = 1.17113710869 rad

Height: ha = 8.29215619759
Height: hb = 6.44989926479
Height: hc = 6.44989926479

Median: ma = 8.29215619759
Median: mb = 6.69895440801
Median: mc = 6.69895440801

Inradius: r = 2.32216373532
Circumradius: R = 4.88444837822

Vertex coordinates: A[9; 0] B[0; 0] C[2.72222222222; 6.44989926479]
Centroid: CG[3.90774074074; 2.1549664216]
Coordinates of the circumscribed circle: U[4.5; 1.98995214708]
Coordinates of the inscribed circle: I[3.5; 2.32216373532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.2299239048° = 134°13'45″ = 0.79988504798 rad
∠ B' = β' = 112.8855380476° = 112°53'7″ = 1.17113710869 rad
∠ C' = γ' = 112.8855380476° = 112°53'7″ = 1.17113710869 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 = 9 ; ; c = 9 ; ;

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

p = a+b+c = 7+9+9 = 25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25 }{ 2 } = 12.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.5 * (12.5-7)(12.5-9)(12.5-9) } ; ; T = sqrt{ 842.19 } = 29.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.02 }{ 7 } = 8.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.02 }{ 9 } = 6.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.02 }{ 9 } = 6.45 ; ;

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**2-9**2-9**2 }{ 2 * 9 * 9 } ) = 45° 46'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-7**2-9**2 }{ 2 * 7 * 9 } ) = 67° 6'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-7**2-9**2 }{ 2 * 9 * 7 } ) = 67° 6'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.02 }{ 12.5 } = 2.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 45° 46'15" } = 4.88 ; ;




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