Given the right triangle below, calculate all missing angles in degrees (round your answer to 3 decimal places.

x = 26.565 ° , y = 63.435 ° x=26.565°,y=63.435° x = 26.565° , y = 63.435°

Given the right triangle below, calculate all missing angles in degrees (round your answer to 3 decimal places.

Welcome back, everyone. So let's give this problem a try. Here we're asked, given the right triangle, calculate all missing angles in degrees, and we're asked to round our answer to 3 decimal places. So let's see how we can do this. Now what I'm gonna do is looking at this right triangle, I'm gonna see if I can first solve for this angle x. And to find x, what we can do is use SOHCATOA. SOHCATOA is this memory tool that we use to relate the trigonometric functions to the sides of the right triangle. Now what I can do is look at our angle x, and I notice that we have the opposite side of this triangle, as well as the adjacent side of this triangle. If If I look at these trigonometric functions, that's going to be the tangent that I need, because tangent is opposite over adjacent. So we can see that the tangent of our angle x is equal to the opposite side of this triangle, which is 3 divided by the adjacent side, which is 6. Now 3 over 6 reduces to 1 half, so we can see that the tangent of x is equal to 1 half. Now solving for x in this equation, all I need to do is take the inverse tangent on both sides. Doing this will get the tangent and the inverse tangent to cancel on the left side, leaving us with just x. And then on the right side we're going to have the inverse tangent of 1 half. Now to solve this problem from here is take the inverse tangent of 1 half and throw this onto a calculator. And if you do this rounding to 3 decimal places, you should get a value of approximately 26.565 degrees. So this right here is the angle x, and that is how we can find one of these missing angles for our right triangle. Now the other missing angle that we need is y. We have that x is 26.565 degrees. And so if we want to find angle y, we can just recognize that all angles in triangle have to add to a 180 degrees. And since this is a 90 degree angle, that means these two angles have to add to 90 degrees. So that means that angle y is simply going to be 90 degrees minus the angle we just calculated of 26.565 degrees. And if you solve this, you should get that your angle y is about 63.435 degrees. So this is going to be the missing angle y. So this is how you can find all the missing angles of this right triangle. Hope you found this video helpful. Thanks for watching.