Week-5

Last week we learned how to use trigonometry to find the missing sides of a right triangle. This week we learned how to find the missing angles, it’s pretty similar, like isolating the variable, and labeling the sides. For me the only big difference is having two measurements of the sides and using them in the equation, we also use the inverse ratios too.

Using trigonometry to find missing angles

Example #1:

Let’s start with a right triangle with a side of 24, longest side is 40 and x° as the acute angle. First, let’s label each side, then look at the measurements given, on the opposite side we have 24 and on the hypotenuse side we have 40. Since, sin ratio has opposite on top and hypotenuse on the bottom, we do the same with the numbers. Now, we have sinxº= and since we need to isolate the “xº” we will move the sin to the other side, when something goes to the other side it becomes the opposite. So now we have xº=sin¯¹(), put it in your calculator and you end up with 36. So, the final answer is xº=36º.

Example #2:

For our second example, we start with a right triangle with a side length of 24.5m and 10m. We have the two shorter side for this one and we need to find the top acute angle. Again, we first label each side, this time we have a tangent ratio because the given measurements are on the opposite and adjacent side. So, start the equation with, tanxº=, then isolate the “x” again and move the tan to the other side. Now we put xº=tan¯¹() into the calculator and we get xº=68º as our answer.