7 20 20 triangle

Acute isosceles triangle.

Sides: a = 7   b = 20   c = 20

Area: T = 68.92197903363
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 20.15773162156° = 20°9'26″ = 0.35218115363 rad
Angle ∠ B = β = 79.92113418922° = 79°55'17″ = 1.39548905586 rad
Angle ∠ C = γ = 79.92113418922° = 79°55'17″ = 1.39548905586 rad

Height: ha = 19.69113686675
Height: hb = 6.89219790336
Height: hc = 6.89219790336

Median: ma = 19.69113686675
Median: mb = 11.15879568022
Median: mc = 11.15879568022

Inradius: r = 2.93327570356
Circumradius: R = 10.15767343224

Vertex coordinates: A[20; 0] B[0; 0] C[1.225; 6.89219790336]
Centroid: CG[7.075; 2.29773263445]
Coordinates of the circumscribed circle: U[10; 1.77774285064]
Coordinates of the inscribed circle: I[3.5; 2.93327570356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.8432683784° = 159°50'34″ = 0.35218115363 rad
∠ B' = β' = 100.0798658108° = 100°4'43″ = 1.39548905586 rad
∠ C' = γ' = 100.0798658108° = 100°4'43″ = 1.39548905586 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 = 20 ; ; c = 20 ; ;

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

p = a+b+c = 7+20+20 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-7)(23.5-20)(23.5-20) } ; ; T = sqrt{ 4749.94 } = 68.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.92 }{ 7 } = 19.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.92 }{ 20 } = 6.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.92 }{ 20 } = 6.89 ; ;

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**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 20° 9'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-7**2-20**2 }{ 2 * 7 * 20 } ) = 79° 55'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-7**2-20**2 }{ 2 * 20 * 7 } ) = 79° 55'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.92 }{ 23.5 } = 2.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 20° 9'26" } = 10.16 ; ;




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