5 9 9 triangle

Acute isosceles triangle.

Sides: a = 5   b = 9   c = 9

Area: T = 21.61545205822
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 32.25552404263° = 32°15'19″ = 0.56329601465 rad
Angle ∠ B = β = 73.87223797868° = 73°52'21″ = 1.28993162536 rad
Angle ∠ C = γ = 73.87223797868° = 73°52'21″ = 1.28993162536 rad

Height: ha = 8.64658082329
Height: hb = 4.80332267961
Height: hc = 4.80332267961

Median: ma = 8.64658082329
Median: mb = 5.72327615711
Median: mc = 5.72327615711

Inradius: r = 1.88795235289
Circumradius: R = 4.68443509489

Vertex coordinates: A[9; 0] B[0; 0] C[1.38988888889; 4.80332267961]
Centroid: CG[3.4632962963; 1.60110755987]
Coordinates of the circumscribed circle: U[4.5; 1.30112085969]
Coordinates of the inscribed circle: I[2.5; 1.88795235289]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7454759574° = 147°44'41″ = 0.56329601465 rad
∠ B' = β' = 106.1287620213° = 106°7'39″ = 1.28993162536 rad
∠ C' = γ' = 106.1287620213° = 106°7'39″ = 1.28993162536 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 = 5 ; ; b = 9 ; ; c = 9 ; ;

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

p = a+b+c = 5+9+9 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-5)(11.5-9)(11.5-9) } ; ; T = sqrt{ 467.19 } = 21.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.61 }{ 5 } = 8.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.61 }{ 9 } = 4.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.61 }{ 9 } = 4.8 ; ;

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{ 5**2-9**2-9**2 }{ 2 * 9 * 9 } ) = 32° 15'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-5**2-9**2 }{ 2 * 5 * 9 } ) = 73° 52'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-5**2-9**2 }{ 2 * 9 * 5 } ) = 73° 52'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.61 }{ 11.5 } = 1.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 32° 15'19" } = 4.68 ; ;




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