# Right Triangle Trigonometry Part 2: Solving for Acute Angles

WHOOO!!!! Bam! Ok, let’s finish this problem.

We have a right triangle and we are looking for an acute angle in this triangle. Now I

have given you all the sides three, four, and five. So, you can use whatever trig function

you like. We are going to use some kind of trig function to find the angle measure of

theta using any two of these three sides since I have given you so much information about

this triangle. How about we just use tangent. We have the tangent of theta equals opposite

over adjacent which is four-thirds. Now we need to get that tangent function away from

theta. If I said two times x equals ten, you would do the inverse of multiplication which

is divide both sides by two and get x equals five. If I said you had x squared equals sixteen,

you would do the inverse function of squaring which is square root both sides and say that

x is equal to plus or minus four. Well, if I want to undo the tangent function I need

to apply the inverse tangent to both sides of the equation…(arctan) I am going to write,

and this middle line may not be necessary for your teacher, but I am going to apply

the inverse tangent

to both sides of this equation. I don’t know why I am working so hard to color code it.

Inverse tangent of four-thirds. The tangent function and the inverse tangent function

will cancel out and that is why this is just a teaching step. You don’t necessarily need

to show this for just doing right triangular trigonometry, Theta is going to be the inverse

tangent of 4/3. Now again, if you want your answers to be in degrees please make sure

that your calculator is in degree mode. The little negative does stand for an inverse

function. Two to the negative one is one half, (2/3) to the negative one power is 3/2, so

a lot of times we see these negative exponents as just flipping the base or moving the base

on which that negative exponent sits on. But, when you talk about functions, this is an

inverse math function. What do you put into a trig function? An angle measure and you

get out, as we can see, the sides of a triangle. With an inverse trig function, you are putting

in the sides of a triangle even if it is just a decimal like one point three repeating.

That decimal that does come from the ratio or the division of two sides of a right triangle.

So the inverse tangent of four-thirds, just type that into your calculator hitting second

or inverse or maybe control and then tangent looking for that little negative one as an

exponent, and type it into your calculator. If you are in degree mode you are going to

get theta is approximately equal to 53.13 degrees. That is how a trig function of sine,

cosine, or tangent will allow you to find the measurements of the acute angles in a

right triangles. If you have one angle… I was going to yell BAM! and get out of here

but, if you have one acute angle and you are totally confident that is correct you subtract

that from 90 to find the other acute angle. Inside a triangle you only have 180 degrees.

So let’s see 90 minus fifty is forty, forty minus three is thirty-seven, and now we have

36.87 degrees. Now I am done… BAM!!! I am Mr. Tarrou:D Go Do Your Homework! Thank you

very much for watching and letting me help. If you are liking my videos please spread

the word and if an ad looks interesting to you, support them please and help me out.

You are welcome! Thanks for watching:)

You did it again, Muchas Gracias!!!

You have the motivation to do your best and get help when needed. You did it again, and I am glad I was there to help a little:)

The only other teacher I know of that has your energy is Ms.Ladd (Go Green Devils!)! Where do you guys get that energy?? And thank by the way, this is really helpful!

Sorry for the delayed reply…somehow you slipped by.

Glad I could help…hope you keep watching and I can keep helping:)

All the energy comes from the LOVE OF TEACHING!!! Thank you:D

such a great teacher !!!

Thank you for saying so:))…and thank you for "liking" my video. Please be sure to spread the word if you continue to find my videos helpful, my growth is supported by viewers like you…thanks for watching!

i logged in my youtube account just yo say thank you you're awesome. ^_^

Thank you for your help, you can teach it a lot faster than my teacher can

And thank you for taking the time to do so!…I really appreciate the comments, they help to keep reminding me why I spend all the time doing them:))

You are welcome and thank you for the show of support and subscribing!…please be sure to share my channel with your friends too:D

you are doing REALLY GOOD JOB!!!

Thank you very much…and thank you too for subscribing!…please share my channel with your friends too:D

Awesome video! Great for college students!!

Thank you…and please feel free to share my channel with as many college students as you can:)

Thanks for the added bonus:)…and I really do appreciate the support of my subscribers! I like the new format and seeing my square on your list of subscribers. It's like seeing your name in lights:D

I think you meant you have 180 degrees inside a triangle at 3:47

Great videos as always Mr Tarrou ðŸ™‚

You're correct…there is 180 degrees inside a triangle. I meant to say in a right triangle the acute angles add to 90 degrees. (just making sure you're paying attention and I see that you were…kudos to you, thanks for catching it!)

And thanks for your continued support:)

thank you for helping me now i understand what my teacher was trying to teach us

Sometimes it just takes a little different version of the same basic steps…I'm glad my version was helpful for you! Feel free to come back and watch my channel anytime:)

The adjacent leg is the leg that helps make the angle you are going to use in your trig function. The hypotenuse is the longest side opposite the right angle…it does not make the right angle.

Thanks, we're using trig functions for AP physics right now and I haven't taken any trig classes yet so your videos are really helpful to me. Thanks again [=

You're welcome…and thanks for supporting by liking and subscribing! I hope you continue to find my videos helpful and if so, please share my channel with your friends and classmates…I have over 400 to choose from:)

Awesome lesson… I have a hard time understanding, what the teacher teaching in class. I now find the right teacher. It's helping me a lot. Thanks for an awesome lesson. You are such a great teacher.!!

ðŸ™‚ That's me smiling after reading your comment! I'm glad you found my channel and find it so helpful. I am honored to be the one helping you learn math and I look forward to a year full of teaching you!

You are legendary ..

I don't know about that YET…but I'll be happy when I see 3 numbers in my subscriber count…and then the next stain will be that "M":) THANKS for subscribing and making that dream ONE number closer!

Keep spreading the word and helping me groW ðŸ˜€

ur aweeesomee

Thank yooooouuuuuuu! And thanks for supporting by choosing, liking and subscribing!

Thank you SOOOO MUCHH! You explained things so thoroughly!!

You are soooo welcome!!! Thanks for choosing my channel to learn from and please tell your friends:)

Thanks a lot! u r great!!

Thank you for the videos, Mr. Tarrou. You're doing a wonderful job.

i keep replaying your intros lol especially for this one

Forever thanking you and the internet for my current A in trigonometry. You have really make a difference in how I think (and feel) about math. Thank you!

I learned a lot from you.. thank you mr…….

you are the best. i wish that my teacher could explain for us as you are doing. Â i will take a quiz on monday and hopefully i will get full mark.Â

such a good teacher learned more in 20 mins than in 2 weeks of math class

There are no words, you were born to teach….

Fantastic job of explaining this thank you

The moment where you are like I understand… maybe Trig is my friend… just maybe

thanks alot it helped but i got confused thoe otherwise thnx alot

This is great stuff and has been extremely helpful in getting me through Trig summer courses (condensed to roughly 8 weeks with class time being used to go through tests/practice problems than Â explaining Â the how or why). I appreciate you taking the time to make these videos, and explain mathematics in an easy to understand way, keep up the amazing work!

Thank you so much ðŸ™‚ since I left school 24 years ago, I've always had to remember if the variable is in the numerator, multiply, if its in the denominator, divide. I have never seen how the equations are derived.

Your best friend in high school if you are taking PreCalc : ProfRobBob ðŸ™‚

Thank you soo much happy to see your vedios …. i have a question can u do the opposite though like by knowing the size of the angle finding the length of a side

these are so helpful.. im taking a class that is self paced… they give you the book and a cd with the curriculum and assignments.. so have to teach myself.. these are so awesome instead of staring at the book trying to figure it out ðŸ™‚

I was wondering, i saw a person in one of your videos ask do you always say BAM in your classes and you said yes. Do you also always say go do your hw at the end of your classes?Â

does 9 + 10 = 21 cause i dont know

so plz help me cause i need to know if 9 + 10 = 21 or 12

This helped me a lot. I am going to take my remedial coz I have bad grades in Math :'( Thanks to you Sir Math wizard. Hope I can pass that remedial :3

In school, I am in algebra 2, but at home I self-study PreCalculus. Thanks so much for these helpful videos, ProfRobBob. I've been going through your PreCalculus playlist for about 5 months now, and it's been a great supplemental resource to my PreCalculus self-study.

I'm from New Zealand, and i have found this and part 1 really helpful, keep it up man!

This is BAM! I never had any teacher like you! Hope you keep on making new videos with more topics I found your channel very helpful your making math easy not like teachers in our university making it harder.

Dude, you should check out Microsoft's calc Mathematics 4.0 if you do a lot on computer. I just downloaded. It graphs in 2d, 3d, has the trig functions all on it. Has a text pad you can type full equations in. Previous computations are saved so you can click them, they appear in your text window, and you can do operations on that number.. it's awesome… free too.

Thank for the tutorial helping me refresh my memory before my year 11 exam

Thank you for the tutorial. It helped me so much! I finally understand my precalculus homework.

FYI Someone else is posting your videos under a few other peoples names

thanks for your videos helped me allot in trigonometry specially in distinguishing the different sides of a triangle ðŸ™‚

great video man helped out a lot

Thank you so much Prof Bob! God bless you ðŸ™‚

professors like you keep my love for math alive, thank you.

THIS KID HELPED ME SO MUCH

WELL FCK U

JOKE!!

GREAT TEACHER BRO

Dude you're the best I totally understand this now!

Thank you a lot! Helped me do better on my tests!

Really helpful video. Come and teach my class please!

THANK YOU PROOF BOB PLSS TAUGTH SOME PHYSICS

you have helped me a lot sir !

I had my college Final today in Trig and I felt like a BOSS! Thank you Prof Rob.

I wish i had you as my teacher

Thank you! By the way, I just subscribed, because THIS is a lot better than my class.

I finally I understand this now, I had no idea this is just a bit easy. I hope I could pass to my final exam and won't repeat Trigonometry again. I wish I had you as my teacher, you're way better than them.

How can I solve this without using a calculator?

DUDE. Thank you for showing that extra step with the arctan at 1:49. My book and teacher did such a horrible job at explaining how that worked. They just basically had us flip tan to the other side and throw a little negative one on it and called it a day. Makes perfect sense now, as i can see that it would be in the denominator on the left side and the two tans would cancel out. Thanks for that unnecessary/necessary step!

thank you , youre a great teacher. i missed school & had no idea how to do this but your videos helped a lot!!

You saved my math grade thank you

i work out the tan inverse of 4 over 3 ,its equal to25.32

it is complicated but not impossible i am having a hard time but i can pull it off

Thx for being a great teacher!

absolutely brilliant

Thank you!!!!! I looked though so many videos and this helped so much.

YOU SAVED MY LIFE SIR!! THANK YOU SOOOO MUCH!

THANK YOU SIR! THANK YOU! I'm GOING TO OUTPLAYED MY EXAMS TOMORROW!

thank you you helped me out

cant explain how helpful this way for me! Thank you so much! You definitely deserve all of the support you were terse, concise, and thoughtful with the ways you tought. BAM!