9.3 Finding the measure of an angle using trig ratios

[00:00:00]hey everybody today we're going to talk about notes 9.3 which is finding the measure of an angle using a trig ratio so 9.2 are all about finding the sides and this one's going to be about finding angles again to make sure just a reminder make sure calculator is in degree mode often abbreviated deg and then you're also going to need to find this button on the calculator a little sign with a little negative one eye it's called the inverse sign or sometimes called arcsin um oftentimes it's on the same button as the sine button itself i'll show you in just a minute here so part a we're going to use our calculator to find the measure of the angle and then it just a brief little reminder if you can't figure out how to get these answers please let us know so we can actually help you with your calculator all right so here's our first example find the measure of the angle and round to one decimal so we have the sine of angle a is equal to 0.6521 so what we can do is we can use the inverse sine to kind of cancel out sine so sometimes i show my kids like just briefly here i just don't like that if you put inverse sine on both sides um it's much like you're actually um you know when you want to divide on both sides it's like it's that process where inverse sine kind of cancels sine on both sides so what you'd be left with you'd be left with the measure of angle a on the left and on the right side we'd have the inverse sine of this decimal which is 0.6521 and that's actually what i want to type in my calculator now so i'm going to pull up my calculator for you guys so again just a brief reminder um you can find these buttons here you can see they're blue on my calculator they're on the actual buttons of sine cosine and tangent but since they're blue i'm going to press the second key first so i'm going to go ahead and press second sine to get my inverse sine button it's the whole sign negative one and i'm going to type in that decimal which is 0.6521 close it uh just a reminder to make sure i am in degree mode and i am you can see the top and i can press enter and it's going to tell me the answer is 40.7 so i'm going to round this to one decimal and call it 40.7 degrees so the measure of angle a is 40.7 degrees let's try this again with cosine so i have cosine of p is going to be equal to 0.4153 again it's just that brief reminder that to get rid of cosine we have to use the inverse cosine on both sides so if i use inverse cosine on both sides i would get the measure of angle b is equal to the inverse cosine of 0.4153 and i just need to go to my calculator and type this in so here we go over the calculator i'm gonna go ahead and press second cosine to get my inverse cosine and get one 0.415 three close that parenthesis press enter and i get 65.5 when i round this one so we're gonna have 65.5 degrees for angle b all right um hopefully you're kind of getting the trend of these things now i'm actually going to leave example c for you to try um and it works just like this you're just going to use inverse tangent all right part b your second type of problem is using a trig ratio to find the measure of an angle and this is involving sohcahtoa now so it says find the measure of an angle round to one decimal so you notice the steps are actually the same steps from our previous notes we want to label the sides set up the trig ratio and solve for x so when i do this let's go ahead and uh label the triangle so um you i wonder where you're going to put your person you're still going to put your person in the actual angle that we have here so that's going to be this spot right there where the x degrees is it's going to have a person i'm going to label the hypotenuse then the adjacent and then the opposite last and again just a brief reminder hypotenuse across from the right angle adjacent next to your person opposite is farthest from your person cross off the one that's not that doesn't have anything and you're left with adjacent so remember from sohcahtoa we're looking at adjacent and hypotenuse so this is a cosine problem so the cosine of x degrees is equal to following uh the k part i see the adjacent and then the hypotenuse okay well this is actually very similar to what we had up above it's just as a fraction instead so what i need to do is use my inverse cosine to get my x out so i just throw this in on both sides just like this all right and uh what i will find out is that x will be equal to the inverse cosine of 4 divided by 11 or 4 11 the fraction if you will so we need to go to our calculator so let's go to the calculator and type this in inverse cosine of four elements so i'm just gonna go second cosine and i'm just gonna type in the fraction four divided by eleven and close it and press enter as i do this i'm going to get the answer to my problem which is sixty eight point seven degrees so x will equal 68.7 degrees and that's all we need all right so um just a little bit of a hint on the back side anytime you are trying to find the angle of sorry find the measure of the angle which is our blank there you'll need to be using the the button with the negative ones you'll be using these inverse trig functions inverse sine inverse cosine inverse tangent so again just reminder these two are on your quick check um and you'll use soca toy to help you set these two problems up i'm actually going to help you get started on the first one here just by labeling get you started a little bit here give you the hint that this is the opposite side and this is the hypotenuse other than that these two are for you let us know if you guys have any questions