5 20 20 triangle

Acute isosceles triangle.

Sides: a = 5   b = 20   c = 20

Area: T = 49.60878370825
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 14.36215115629° = 14°21'41″ = 0.25106556623 rad
Angle ∠ B = β = 82.81992442185° = 82°49'9″ = 1.44554684956 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 19.8433134833
Height: hb = 4.96107837082
Height: hc = 4.96107837082

Median: ma = 19.8433134833
Median: mb = 10.60766017178
Median: mc = 10.60766017178

Inradius: r = 2.20547927592
Circumradius: R = 10.07990526136

Vertex coordinates: A[20; 0] B[0; 0] C[0.625; 4.96107837082]
Centroid: CG[6.875; 1.65435945694]
Coordinates of the circumscribed circle: U[10; 1.26598815767]
Coordinates of the inscribed circle: I[2.5; 2.20547927592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6388488437° = 165°38'19″ = 0.25106556623 rad
∠ B' = β' = 97.18107557815° = 97°10'51″ = 1.44554684956 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 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 = 20 ; ; c = 20 ; ;

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

p = a+b+c = 5+20+20 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-5)(22.5-20)(22.5-20) } ; ; T = sqrt{ 2460.94 } = 49.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.61 }{ 5 } = 19.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.61 }{ 20 } = 4.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.61 }{ 20 } = 4.96 ; ;

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**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 14° 21'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-5**2-20**2 }{ 2 * 5 * 20 } ) = 82° 49'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-5**2-20**2 }{ 2 * 20 * 5 } ) = 82° 49'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.61 }{ 22.5 } = 2.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 14° 21'41" } = 10.08 ; ;




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