# 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…

ARCSIN (**A**/**HYP**)

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…

=ASIN (30/192)

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))

## Conclusion:

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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## Comments 1 comment

Hi David, I thought HYP times CosX=B. Since B and HYP are known, X could be figured out. Or X=Cos inverse B/HYP? Have I got that right?

You've got some remarkable articles right here! Cheers!