given a circle with radius r, a "vertical" radius of v and a horizontal object length n on the top of the circle, is it possible to find the length of the object if the angle from the circle centre to the left edge of the object is known?
+23251 Possibly --
Isn't the vertical radius (v) the same as the radius (r)?
Do you know where the horizontal object is balanced on the circle? Is it balanced in the middle?
If it is balanced in the middle then its length from the center to the left edge is n/2.
There is a right triangle formed from the center of the circle to the top of the circle to the left end of the object.
Call the distance from the center to the left end d.
Then use the Pythagorean Theorem; d represents the length of the hypotenuse; so d^2 = v^2 + (n/2)^2.
Thus d^2 - v^2 = (n/2)^2.
---> n/2 = sqrt( d^2 - v^2 )
---> n = 2 * sqrt( d^2 - v^2 )
+23251 Possibly --
Isn't the vertical radius (v) the same as the radius (r)?
Do you know where the horizontal object is balanced on the circle? Is it balanced in the middle?
If it is balanced in the middle then its length from the center to the left edge is n/2.
There is a right triangle formed from the center of the circle to the top of the circle to the left end of the object.
Call the distance from the center to the left end d.
Then use the Pythagorean Theorem; d represents the length of the hypotenuse; so d^2 = v^2 + (n/2)^2.
Thus d^2 - v^2 = (n/2)^2.
---> n/2 = sqrt( d^2 - v^2 )
---> n = 2 * sqrt( d^2 - v^2 )
