The fence

I'm building a cloth (board) fence. The boards are rounded in a semicircle at the top. The tops of the boards between the columns should copy an imaginary circle. The tip of the first and last board forms the chord of a circle whose radius is unknown. The length of the circle string is 180cm. The arc height "in the middle" of the string is 23cm. The boards are 16, and their axes are 12 cm apart. Please calculate the heights of board numbers 2 to 8, i.e., half the arc.

Correct answer:

r =  187.6 cm
y2 =  170.6 cm
y3 =  175.6 cm
y4 =  179.6 cm
y5 =  182.8 cm
y6 =  185.2 cm
y7 =  186.7 cm
y8 =  187.5 cm

Step-by-step explanation:

r2=(180/2)2+(r23)2 r=(8100+529)/46=187.6 cm
(1290)2+(y2)2=r2 y2=170.6 cm
(2490)2+(y3)2=r2 y3=175.6 cm
(3690)2+(y4)2=r2 y4=179.6 cm
(4890)2+(y5)2=r2 y5=182.8 cm
(6090)2+(y6)2=r2 y6=185.2 cm
(7290)2+(y7)2=r2 y7=186.7 cm
(8490)2+(y8)2=r2 y8=187.5 cm



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Do you want to convert length units?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: