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Calculate the angle of a right triangle - Trigonometry for Gazebo
Right Angle Calculations
Is There Math Out Here?
One of the things I enjoy most (other than programming) is the periodic opportunities I get to spend some time at my family’s getaway up north in Minnesota. We have a 20 acre piece of woodland paradise with a small cabin. There are lots of trails to walk; creeks running through the property, hunting, and four wheeling, camping, and well… you get the point.
Trigonometry in the woods:
A few years ago, my brothers and our dad built a platform-deck with a raised square gazebo in its corner which is where my beautiful fiancé and I will be wed in August this year. So in preparation for the festivities, my brother Harvey and I were preparing some calculations for the construction of a wheelchair ramp leading up to the deck surface.
How Steep is That Thing Anyway?
Having taken trigonometry many years ago, Harvey asked me if I could figure out what the angle of the ramp would be with a 30” rise and a length along the slanted surface (hypotenuse) of 16 feet.
I did a little research – like I said, it’s been a long time since I’ve done trig – and found that the formula is basically…
Let A = 30” rise
Let HYP = 192” (the 16 feet along the inclined surface of the ramp divided by 12”).
For most calculators you would enter 30 / 192 then press [INV] [SIN] and presto! You have your angle. However, Harvey likes to use Microsoft Excel to do his calculations so I had to figure out how to get these results with Excel. So, I quickly threw together a cell with the following formula…
But wait! Why am I not getting 8.9893 deg. Like I did with my calculator? What the heck is this 0.1569 that I keep coming up with?
Well, it turns out that Excel (along with most programming languages) performs trigonometric calculations based on Radians, not degrees. Once I figured that out, I quickly searched for help on how to convert radians to degrees in Excel. You would be amazed at how easy it is.
LET cell A1 = 30
Let cell B1 = 192
In cell C1 put the following formula =DEGREES (ASIN (A1/B1))
It’s that simple! Really, it is. So now we know that the angle of our proposed wheelchair ramp will be roughly 9°.
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