How to... find the size of an interior angle of a right triangle using sin/cos/tan

So yesterday's post was working with right triangles and trig functions when you know the interior angles and you have the length of one side of the triangle, but what about if you want to find the size of an interior angle? Well, we use the same trig functions - sin/cos/tan - as we do if we're trying to find the length of a side except we use the inverse.


By using the inverse functions we can find the size of the interior angle. It's important when you're doing this to make sure you still get your SOH CAH TOA correct and pay special attention to which side is the opposite (O) or adjacent (A) side in relation to whichever angle you're wanting to find. It's a common mistake to go "oh, I use sine" and then switch up the O, A or H. This is particularly common if there is a drawing and the right triangle is positioned with the hypotenuse facing the bottom of the page, like this...



Anyway, here's an example of using inverse trig functions -

Now, if you put this into your calculator it will probably return the answer 36.8698 etc.

Generally we don't talk about degrees with decimals, but rather as degrees and minutes. Just like with time, there are sixty minutes in one degree as there are sixty minutes in one hour. To change it on your calculator to read as degrees and minutes rather than with a decimal, find the button on your calculator that looks like it is a couple of apostrophes and degrees signs (the little bubble apostrophe thing :) ). It may be different on different calculators, so play around with it and you'll know when you've found it because it will change your answer to read as degrees and minutes. Don't wait for an exam situation to do this :)

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