7 7 9 triangle

Acute isosceles triangle.

Sides: a = 7   b = 7   c = 9

Area: T = 24.12985619132
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 49.99547991151° = 49°59'41″ = 0.87325738534 rad
Angle ∠ B = β = 49.99547991151° = 49°59'41″ = 0.87325738534 rad
Angle ∠ C = γ = 80.01104017697° = 80°37″ = 1.39664449467 rad

Height: ha = 6.89438748323
Height: hb = 6.89438748323
Height: hc = 5.36219026474

Median: ma = 7.26329195232
Median: mb = 7.26329195232
Median: mc = 5.36219026474

Inradius: r = 2.09881358185
Circumradius: R = 4.56992735604

Vertex coordinates: A[9; 0] B[0; 0] C[4.5; 5.36219026474]
Centroid: CG[4.5; 1.78773008825]
Coordinates of the circumscribed circle: U[4.5; 0.7932629087]
Coordinates of the inscribed circle: I[4.5; 2.09881358185]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.0055200885° = 130°19″ = 0.87325738534 rad
∠ B' = β' = 130.0055200885° = 130°19″ = 0.87325738534 rad
∠ C' = γ' = 99.99895982303° = 99°59'23″ = 1.39664449467 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 = 7 ; ; c = 9 ; ;

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

p = a+b+c = 7+7+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 * (11.5-7)(11.5-7)(11.5-9) } ; ; T = sqrt{ 582.19 } = 24.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.13 }{ 7 } = 6.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.13 }{ 7 } = 6.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.13 }{ 9 } = 5.36 ; ;

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**2-7**2-9**2 }{ 2 * 7 * 9 } ) = 49° 59'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-7**2-9**2 }{ 2 * 7 * 9 } ) = 49° 59'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 80° 37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.13 }{ 11.5 } = 2.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 49° 59'41" } = 4.57 ; ;




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