14 20 20 triangle

Acute isosceles triangle.

Sides: a = 14   b = 20   c = 20

Area: T = 131.1454957966
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 40.97546302294° = 40°58'29″ = 0.71551422073 rad
Angle ∠ B = β = 69.51326848853° = 69°30'46″ = 1.21332252231 rad
Angle ∠ C = γ = 69.51326848853° = 69°30'46″ = 1.21332252231 rad

Height: ha = 18.73549939952
Height: hb = 13.11444957966
Height: hc = 13.11444957966

Median: ma = 18.73549939952
Median: mb = 14.07112472795
Median: mc = 14.07112472795

Inradius: r = 4.85772206654
Circumradius: R = 10.67552102537

Vertex coordinates: A[20; 0] B[0; 0] C[4.9; 13.11444957966]
Centroid: CG[8.3; 4.37114985989]
Coordinates of the circumscribed circle: U[10; 3.73663235888]
Coordinates of the inscribed circle: I[7; 4.85772206654]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0255369771° = 139°1'31″ = 0.71551422073 rad
∠ B' = β' = 110.4877315115° = 110°29'14″ = 1.21332252231 rad
∠ C' = γ' = 110.4877315115° = 110°29'14″ = 1.21332252231 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 = 14 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 14+20+20 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-14)(27-20)(27-20) } ; ; T = sqrt{ 17199 } = 131.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.14 }{ 14 } = 18.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.14 }{ 20 } = 13.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.14 }{ 20 } = 13.11 ; ;

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{ 14**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 40° 58'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-20**2 }{ 2 * 14 * 20 } ) = 69° 30'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 69° 30'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.14 }{ 27 } = 4.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 40° 58'29" } = 10.68 ; ;




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