9 20 20 triangle

Acute isosceles triangle.

Sides: a = 9   b = 20   c = 20

Area: T = 87.69222887146
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 26.00657563258° = 26°21″ = 0.45438860724 rad
Angle ∠ B = β = 76.99771218371° = 76°59'50″ = 1.34438532906 rad
Angle ∠ C = γ = 76.99771218371° = 76°59'50″ = 1.34438532906 rad

Height: ha = 19.48771752699
Height: hb = 8.76992288715
Height: hc = 8.76992288715

Median: ma = 19.48771752699
Median: mb = 11.85332695911
Median: mc = 11.85332695911

Inradius: r = 3.57992770904
Circumradius: R = 10.26331601158

Vertex coordinates: A[20; 0] B[0; 0] C[2.025; 8.76992288715]
Centroid: CG[7.34216666667; 2.92330762905]
Coordinates of the circumscribed circle: U[10; 2.30992110261]
Coordinates of the inscribed circle: I[4.5; 3.57992770904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9944243674° = 153°59'39″ = 0.45438860724 rad
∠ B' = β' = 103.0032878163° = 103°10″ = 1.34438532906 rad
∠ C' = γ' = 103.0032878163° = 103°10″ = 1.34438532906 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 = 9 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 9+20+20 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-9)(24.5-20)(24.5-20) } ; ; T = sqrt{ 7689.94 } = 87.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87.69 }{ 9 } = 19.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87.69 }{ 20 } = 8.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87.69 }{ 20 } = 8.77 ; ;

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{ 9**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 26° 21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-9**2-20**2 }{ 2 * 9 * 20 } ) = 76° 59'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-9**2-20**2 }{ 2 * 20 * 9 } ) = 76° 59'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87.69 }{ 24.5 } = 3.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 26° 21" } = 10.26 ; ;




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