My Math Forum Converting angle in inches to degrees

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 June 4th, 2018, 03:17 AM #1 Newbie   Joined: Aug 2015 From: USA Posts: 17 Thanks: 0 Converting angle in inches to degrees Hi forum, my window air conditioner instructions indicate that the unit must be tilted back 1/4" for proper drainage. I'd like to figure this out in degrees, since I took a college trig a few years ago and feel like I should know how to solve something so basic. My initial attempt has me drawing a unit circle with with a right angle measuring .25 on the y axis. How to approach this problem? Thanks in advance.
 June 4th, 2018, 05:29 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,747 Thanks: 2133 The instructions are ambiguous, as they do not state which part of the air conditioner has to move 1/4” when the air conditioner is tilted.
 June 4th, 2018, 06:23 AM #3 Newbie   Joined: Aug 2015 From: USA Posts: 17 Thanks: 0 Hi, a window air conditioner is one, self-contained unit that tilts back so that excess condensate drains outside. The tilt of the unit is specified as 1/4" angle downward (to the outside). If someone might help me get started converting that 1/4" tilt to a degree angle I'd be most appreciative.
June 4th, 2018, 07:28 AM   #4
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 Originally Posted by paulm Hi, a window air conditioner is one, self-contained unit that tilts back so that excess condensate drains outside. The tilt of the unit is specified as 1/4" angle downward (to the outside). If someone might help me get started converting that 1/4" tilt to a degree angle I'd be most appreciative.

Assuming the air conditioner is hinging on the bottom mating corner, we'd need to know the length of the unit to calculate the angle. However measuring total inch drop at the back of the unit is more accurate in all practicality.

 June 4th, 2018, 07:33 AM #5 Math Team     Joined: Jul 2011 From: Texas Posts: 2,947 Thanks: 1555 What is the distance from the front to the rear of the unit along the bottom? Thanks from paulm
June 4th, 2018, 09:13 AM   #6
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 Originally Posted by skeeter What is the distance from the front to the rear of the unit along the bottom?
Thanks, that got me started. The back-half of unit is already angled, and instructions indicate measuring from where window meets the angled part. So the angled back-half of unit is 7.8". I found the last (adjacent) side of triangle through Pythag. Ther. (1/4)^2 + x^2 = (7.8 )^2, thus adjacent side = 7.79, and then solving cos = .998 and acos = 3.62°, which is exactly the angle of back-half of unit, using bubble level.

Basically the unit could be level (but not at all tilting forward) and drain properly, given the already-angled back.

I wanted to know how to approach this using trig so thanks for reminding me how to get started.

Last edited by paulm; June 4th, 2018 at 09:16 AM.

 July 14th, 2018, 09:44 AM #7 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 I would have done this a little differently. If the height of the air conditioner (measured from top to bottom) is "h" inches then the angle is given by $\displaystyle \sin(\theta)= \frac{\frac{1}{4}}{h}= \frac{1}{4h}$ so $\displaystyle \theta=\arcsin\left(\frac{1}{4h}\right)$. But I must say that I think that, as a practical matter, you will find it easier to measure the "1/4 inch" than the angle. Last edited by skipjack; July 14th, 2018 at 11:33 PM.
 July 19th, 2018, 06:45 AM #8 Newbie   Joined: Jul 2018 From: tn. Posts: 4 Thanks: 0 using 7.8" as the hypotenuse and .25" as the opposite leg figure the angle using square root. square 7.8" = 60.84 or (7.8" times itself). Hypotenuse side square .25" = .0625 Opposite side subtract .25 from 60.84 = 60.7775 get square root of 60.7775 = 7.79599256" Adjacent side divide .25 by 7.8 = .032051282 this is SINE of the smallest angle of this right angle divide .25 by 7.79599256 = .032067757 this is TANGENT of this angle inverse Sine (.032051282) = 1.836717753 or decimal degree of angle inverse TANGENT (.032067757) = 1.836717753 or decimal degree of angle using calculator put in 1.836717753 (D.D.) then degree, minutes, seconds key = 1 degree 50 minutes and 12.18 seconds this will be the tilt angle for your air cond.

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