4 9 9 triangle

Acute isosceles triangle.

Sides: a = 4   b = 9   c = 9

Area: T = 17.55499287748
Perimeter: p = 22
Semiperimeter: s = 11

Angle ∠ A = α = 25.67991768138° = 25°40'45″ = 0.44881861846 rad
Angle ∠ B = β = 77.16604115931° = 77°9'37″ = 1.34767032345 rad
Angle ∠ C = γ = 77.16604115931° = 77°9'37″ = 1.34767032345 rad

Height: ha = 8.77549643874
Height: hb = 3.98999841722
Height: hc = 3.98999841722

Median: ma = 8.77549643874
Median: mb = 5.31550729064
Median: mc = 5.31550729064

Inradius: r = 1.59554480704
Circumradius: R = 4.61554033466

Vertex coordinates: A[9; 0] B[0; 0] C[0.88988888889; 3.98999841722]
Centroid: CG[3.29662962963; 1.32999947241]
Coordinates of the circumscribed circle: U[4.5; 1.02656451881]
Coordinates of the inscribed circle: I[2; 1.59554480704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.3210823186° = 154°19'15″ = 0.44881861846 rad
∠ B' = β' = 102.8439588407° = 102°50'23″ = 1.34767032345 rad
∠ C' = γ' = 102.8439588407° = 102°50'23″ = 1.34767032345 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 = 4 ; ; b = 9 ; ; c = 9 ; ;

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

p = a+b+c = 4+9+9 = 22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22 }{ 2 } = 11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11 * (11-4)(11-9)(11-9) } ; ; T = sqrt{ 308 } = 17.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.55 }{ 4 } = 8.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.55 }{ 9 } = 3.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.55 }{ 9 } = 3.9 ; ;

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{ 4**2-9**2-9**2 }{ 2 * 9 * 9 } ) = 25° 40'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-4**2-9**2 }{ 2 * 4 * 9 } ) = 77° 9'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-4**2-9**2 }{ 2 * 9 * 4 } ) = 77° 9'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.55 }{ 11 } = 1.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 25° 40'45" } = 4.62 ; ;




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