Trigonometry Pt 3 - Angles of Elevation and Depression

[@aamarahb6367]

the angles of depression gave me depression so im the person sitting at the top of a building lol

[@RealMikeDobbs]

Well, take heart because the angle of depression and the angle of elevation are congruent, so even when you feel like you're looking down, you're also the person looking up to a bright future : )

[@ToxicServalFox]

I almosted spit my drink om- b ro

[@goputad3015]

@@RealMikeDobbs You've banged it there with that reply, fair play mate

[@mustafa-pv9tl]

How old r u

[@meshachgopaul1077]

@@RealMikeDobbs an outstanding reply worthy of an award mike

[@lenaalsaadi-wi6eq]

Tomorrow I have a math exam, and I was so stressed, but after watching your videos, I understood everything. All the love from Saudi Arabia

[@RealMikeDobbs]

That’s terrific to hear, I’m so glad it helped you. Thanks for letting know 😀

[@14oznalgenewaterbottle]

lol who's here cause they're studying for their test tomorrow :)

[@roche1517]

Me

[@krishpatwari3369]

Factz

[@triz23712]

My retake ;_;

[@deaisha4402]

Me😂

[@miffyluvbug]

*10 minutes

[@AngraMan]

I used to get totally confused to work out the angle of depression and evaluation but now from your video I get to understand and I want more of your video. Thanks

[@RealMikeDobbs]

Oh that's terrific. Thanks so much for letting me know, I'm glad the video helped you understand 😄

[@mikuculus3720]

This was really helpful! Granted, I knew all the information, just didn’t know how to set up the problem, which is like the main part. Great video!

[@RealMikeDobbs]

Thanks very much- awesome to hear that it helped you out 👍

[@5O_YT]

hey u remember this vid💀

[@waltonleer]

my teacher didn't even mention the fact that you have to keep the angle of depression outside of the original triangle. tysm I finally understand this topic

[@RealMikeDobbs]

That's terrific- glad the video helped you. Thanks for letting me know 😄

[@reddiredd3]

Really easy and straight forward, this video helped me to visualize the idea of what is really meant by the Angles of Elevation and Depression, that horizontal line was so much important.

[@RealMikeDobbs]

Thanks so much for letting me know- glad to hear it helped you out 😀

[@sully5494]

Such an amazing teacher. I got confused in class since there's less time with this whole covid thing but this cleared everything up.

[@RealMikeDobbs]

Wow- thanks very much, I’m so glad to hear it helped you 😀

[@ASAPlizzo969]

True my g

[@martinevans5052]

This teacher did not just made this easy for me in just 13 minutes...WoW thank you sir

[@RealMikeDobbs]

Haha- so glad you found it helpful 😀

[@wonderpanda1630]

I love how clear you were and how you explained what you did!!

[@RealMikeDobbs]

Why thank you! So glad you found it helpful 😀

[@rShack1001]

MIKES DOBBS U DA GOAT FOR REAL IM GONNA PASS MY TEST BECAUSE OF YOU!!!!!!!!!!!!!!

[@RealMikeDobbs]

Wow- thanks so much! So glad to hear it helped you. Best of luck on your test 😀

[@abubakarrsesay2511]

It teaches me a lot and help me to now solve questions on this topic Thank you so much as I am grateful

[@RealMikeDobbs]

You’re very welcome- glad to hear it helped you out 👍

[@danielflint3676]

Easily understood because of clear explaination.

[@RealMikeDobbs]

Thanks so much- I'm glad it helped you out 😄 👍

[@aryannargotra153]

Thank you so much you helped me understand it so clearly. Now I can give my exam with confidence tomorrow.

[@RealMikeDobbs]

That’s terrific- thanks so much for letting me know 😀

[@mookertz6889]

Really Simple and Straight to the Point, Love the videos and keep up the Amazing work.

[@RealMikeDobbs]

Thanks so much, glad to know it helped you out 😀

[@mookertz6889]

@@RealMikeDobbs I got a Perfect Score on My Exam 😊 thank you so much 🙏

[@RealMikeDobbs]

Congratulations- that's fantastic 😄

[@PastaZ0neAct1]

Thank you so much for being able to understand trig. You have saved my grades

[@RealMikeDobbs]

Hey thanks, glad to hear it helped 😄

[@adoboiehinds]

this was a very helpful video because I never quite understood this topic but thanks to you i do now and because of that you just gained a follower.

[@RealMikeDobbs]

Thank you so much 😀 Glad to hear the video helped you.

[@Stayposiv]

The questions that you used oddly were similar to the ones I had that I didn't understand making this 10× easier fir me

[@RealMikeDobbs]

Hey that's great! Glad it helped 😄

[@leahcg]

i was looking for some extra practice problems and this video was great to practice and check my work with! thank you so much!

[@RealMikeDobbs]

Thanks for letting me know- love hearing that my work helps people 😀

[@user-oj6to8fs8n]

life savor for real. i loved the way you explained the problem. thank you 🙏🙏🙏

[@RealMikeDobbs]

You’re so very welcome! Thanks for letting me know 😀

[@booksland8940]

Excellent explanation in shortest possible time

[@RealMikeDobbs]

Thank you so much 😄

[@KoroyinBlessing]

It is also helping me for my assignment and test

[@RealMikeDobbs]

That’s great to hear- thanks for letting me know 😀

[@danmike2305]

Thanks for the informative trigonometry lesson.

[@RealMikeDobbs]

You're so very welcome- glad you found it helpful 😄

[@harlanshafer3429]

Very well presented. I'm doing this for kicks, and it's applicable to Celestial Navigation.

[@RealMikeDobbs]

Thanks very much 😄 Sounds like an interesting application.

[@RealMikeDobbs]

That's terrific, I'm glad it helped you. Thanks for letting me know 😄

[@ninilyn2518]

thank you i have a test tommorrow and didnt understand a thing when my teacher did it this was very helpfull

[@RealMikeDobbs]

That's terrific Nini- so glad it helped you out 😄

[@adahgideono.924]

Me too😑

[@lordoftheeggz5258]

I'm gonna Cry I FINALLY GET IT THANK YOU 😭

[@RealMikeDobbs]

Oh wow- you’re so very welcome. I’m so glad it helped you out 😀

[@SamuelYehirai]

Thank you I watch for Papua New Guinea and that really helps me .I am so grateful 🙏🙏🙌😁

[@RealMikeDobbs]

Wow- so cool that people from all over the world can benefit from these. Glad to hear it helped you out- thanks for letting me know 😄

[@Julux_28]

Wow amazing video! I understood so well!

[@RealMikeDobbs]

That's fantastic- thanks for letting me know 😄

[@jmassoud2526]

this video was so helpful! thank you so much!

[@RealMikeDobbs]

So good to hear, thank you 😄

[@devpatel3560]

I like this guy he explained well

[@RealMikeDobbs]

Thanks so much 😀

[@aaayjaay4412]

i think you are mistaken with the last question, yes rounded off the answer is 5,7 but the ratio is tan not sine, the distance from the hot air balloon to the house is the horizontal length not the diagonal length.

[@RealMikeDobbs]

Hi- thanks for watching and for the comment. This does sometimes trip students up at first, as they want to measure the distance along the ground. However, the distance from the hot air balloon to the house is the length of a line segment connecting those two points (the balloon and the house). If you were to draw that line on the picture it would go through the air, not along the ground. The distance you're thinking of (along the ground) is the distance from a point on the ground directly under the balloon to the house. Does that make sense?

[@aaayjaay4412]

@@RealMikeDobbs thanks for the response, but so what if its not at the same elevation as the hot air balloon, its still a distance, lets say this was on a cartesian plane, the x values from house to balloon should be the distance, however high the balloon is... shouldn't matter

[@RealMikeDobbs]

I understand what you're saying, it sounds to me like you are confusing the "horizontal distance" with the actual distance from the house to the hot air balloon. If it were as you say, then no matter how high the balloon goes the "distance to the house from the balloon" would stay the same. This is of course, not true. I made a short little animation for you (on a Cartesian plane). Take a look at it. The red line is the distance from the balloon to the house. The blue line is the "horizontal distance" from the balloon to the house. The only time those two distances are ever the same is when they are at the same vertical position on the plane. Does this help? kzbin.info/www/bejne/pZvZl6CLqNCZmqc

[@aaayjaay4412]

@@RealMikeDobbs i see, thank you for the clarification

[@RealMikeDobbs]

You're very welcome, I'm glad it helped 😄

[@fatimahadid1730]

Thankkk uuuuu soooo much You saved my life 😭💘

[@RealMikeDobbs]

So glad it helped you out 😀

[@thevividace1816]

i cant get over how he drew the eagle at 3:50

[@shrutikallideen8845]

Thank you so much. So helpful!

[@RealMikeDobbs]

You’re very welcome 😀

[@davidhill8163]

Many thanks this was a great help as I was tripping up on the angle of depression

[@RealMikeDobbs]

You’re very welcome! I love hearing about how these vids help people. Thanks for watching and commenting 😀

[@14oznalgenewaterbottle]

UR SO GOOD AT THIS THANKS!!

[@RealMikeDobbs]

Thank you! 😀

[@HarmonyTheKF]

I appreciate you and this explanation thank you so much!

[@RealMikeDobbs]

Thank you so much! I’m so glad you found it helpful 😀

[@Big_codex]

Thanks man, you made my day ❤️

[@RealMikeDobbs]

How nice to hear 😄 Glad the video helped you out ❤️

[@antocop4432]

thank you, this was really helpful!

[@RealMikeDobbs]

Thanks for watching- so glad it helped you out 😄

[@Evan_Schewe]

Super duper easy! love the drawings too

[@Evan_Schewe]

Also sorry i have a test tommorow but im note understanding how the 10,000ft away at the end is on the sideways line inside of the ground? wouldnt it be if you. OH Shoot as im typing this im thinking and now i understand. Its because the little stick dude is all the way in a air ballon. not on the ground

[@RealMikeDobbs]

Sounds like you figured it out. Glad the video helped you, hope that test went well 😀

[@AfroGirl5852]

This video is so helpful thank you!!!❤

[@RealMikeDobbs]

You're very welcome- thanks for letting me know it helped you 😄

[@SovietBorderLine]

Great vid mate!

[@RealMikeDobbs]

Thanks!

[@olabunmisamuel3189]

Thank you sir it really helps me for my exam

[@RealMikeDobbs]

You're very welcome- thanks for commenting 😄

[@akwithyou1066]

Thank you so much it was real helpful

[@RealMikeDobbs]

That’s great to hear- thank you 😀

[@deancabalfin9835]

Thanks for the tutorial!, although the Eagle was a bit sus Lol.

[@RealMikeDobbs]

Haha, I draw terrible pictures, that's why I became a math teacher 🤣 Glad it helped you out 😄

[@Jose_814]

why is it 53 too? Isn't the angle of depression and elevation both sum 90°?

[@RealMikeDobbs]

That's a common mistake. If you rewatch the first two minutes of the video, you will see that the angle of elevation and the angle of depression are alternate interior angles to each other, and therefore always the same measure. The key is that they are both measured from horizontal. Hope that helps 😄

[@Jose_814]

@@RealMikeDobbs thank you

[@haldenkepple4242]

How many feet would the first major hill in the (Fast And Furious: New England) arcade game incline up if it were in real life?

[@RealMikeDobbs]

That would be interesting to try to work out based on observations made in the game

[@rumbidzaichikasha3019]

i want to know how to use the caculator while working this out

[@RealMikeDobbs]

The first video in my Trig series covers that: kzbin.info/www/bejne/pYDSiJp7mN6Mp9U

[@rumbidzaichikasha3019]

@@RealMikeDobbs thank you

[@hawaahmed8386]

Thanks so much ❤️ you've helped me a lot srsly

[@RealMikeDobbs]

You're very welcome! Glad to hear it helped 😄

[@adhamsalah4530]

Thanks alot mate helped me for the test😀

[@RealMikeDobbs]

You're welcome- glad to know it helped 😄

[@musiceditsgeorgemichlarchi2058]

One paper this works since angle and one length is given but in real life, if given the hyponuese, angles becomes useless. Climbing a tree is easier than using a tiny protractor on meters long paper to measure angle.

[@RealMikeDobbs]

Hey, thanks for watching and commenting 😀 I’m not sure I follow exactly what you’re saying. In practice it’s much easier to measure angles in real life than it is to measure distances. I suppose it all depends on what you’re trying to do. These days if you wanted to know how tall something is you could just send up a drone with an altimeter- but if you go back 40 years or so, it would be much easier and more practical to measure a distance away from the tree on the ground and then measure the angle of elevation and use some trig. That’s more or less how all maps were created before we had GPS. Surveyors would pace or measure out distances along the ground, and then measure angles between points to calculate other distances. Climbing tall objects also introduces many risks that walking on the ground does not. It’s also worth noting these are sanitized examples designed to allow HS students to practice basic skills and don’t accurately represent the many additional complications you would encounter in the real world. For example, over long enough distances you need to start taking the curvature of the earth into account depending on how accurate you need your eventual calculations to be.

[@haleyschnars7569]

thank u my king

[@RealMikeDobbs]

You're very welcome 😄

[@yolandajoseph9450]

This really helped me

[@RealMikeDobbs]

Great to hear- thank you 😀

[@Charles-wr7xx]

using this to study ty mr a

[@RealMikeDobbs]

Awesome! 👍

[@akhilchakravarthy2332]

Thank you so much

[@RealMikeDobbs]

You’re very welcome! Glad it helped you out 😀

[@rophinamartins1743]

I understand 😊😊😊😊

[@RealMikeDobbs]

That's terrific- so glad it helped you out 😄

[@aminasuriya2524]

Hi I am sorry to ask that but I didn't understand how did u got 353

[@RealMikeDobbs]

That's just plugging into the calculator and using the Tangent function. If you aren't sure how to do that, you may want to check out my trig introduction video: kzbin.info/www/bejne/pYDSiJp7mN6Mp9U

[@MariamAhmedHusseinAbdElbary]

that is great i got it !!

[@RealMikeDobbs]

Fantastic 😄

[@txseka-es3cg]

I GET IT NOW!!!!!

[@RealMikeDobbs]

Awesome! Glad it helped you out 😀

[@teiju4614]

My Math Project brings me here 😂

[@teiju4614]

FOR ROBLOX COMMUNITY 😂😂

[@RealMikeDobbs]

Hooray! Hope you found it helpful 😀

[@laural525]

Thank you!

[@RealMikeDobbs]

You’re very welcome 😀

[@Leo-gv4jo]

This helped because i have a test in a few hours and i realized i never learnt the work idk i didnt get the memo we did this apparently

[@RealMikeDobbs]

Well I'm glad to have been able to help. Good luck on your test 😄

[@Leo-gv4jo]

@@RealMikeDobbs ive already finished the test and im 100% sure i got that question right

[@RealMikeDobbs]

Way to go!

[@ASAPlizzo969]

Bro read my mind

[@MosammetRim]

thanks sir

[@RealMikeDobbs]

You’re very welcome- glad you found it helpful 😀

[@kaeelle]

9:29 leaning tower of pisa

[@RealMikeDobbs]

That's fair 🤣 I'm better at math than at drawing, but as I always tell my students: it doesn't matter if your picture is good, it only matters if it's useful.

[@isetmysononfire]

good video

[@RealMikeDobbs]

Thank you 😀

[@ponzas6229]

I got 247 for the first problem, I put 150Tan(67)=

[@RealMikeDobbs]

Easy fix- you’re in Radian (Rad) mode. Radians are a different way to measure angles. You need to change your calculator to degree mode when working in degrees.

[@14oznalgenewaterbottle]

my takeaway from the vid: ALWAYS DRAW THAT HORIZONTAL LINE!

[@RealMikeDobbs]

Yes! There ya go 👍

[@luthandongcobo6550]

he is really good at this but I had a problem with him talk to fast for me to even calculate for myself and try to see if I understand and maybe u should maybe give us a minute to try and answer the question

[@RealMikeDobbs]

Thanks for watching 😀 I’m sorry you felt the pace was too fast. Since everyone works at a different pace- what I try to do is keep the video moving with the understanding that you can pause at any time. When working through the problems in a video I would recommend you pause it after the problem has been presented. Try to set it up yourself, then play forward and see if you set it up the way I did. Then, pause again before I work out the Algebra and do your own Algebra. Then play to see if we arrived at the same result. Otherwise the videos become too long and I feel a lot of people won’t watch an hour long video on a topic.

[@luthandongcobo6550]

@@RealMikeDobbs Now I understand why u fast but u really good at this and I learn't a lot on the video and want to thaank u for making me understand the concepts

[@RealMikeDobbs]

Thanks so much- I’m really glad the videos are helping you understand 😀

[@MamatSarge]

❤❤

[@jamalwilson8952]

Use full video

[@RealMikeDobbs]

Why thank you 😄

[@hollanddd9045]

Lol who’s here while taking there test✋🏼

[@5O_YT]

Who else here from Mr Macintosh class🤣 at st jago

[@rushdonztevi3739]

Mm

[@kiyoshinguyen6213]

You Kinda Sound like Tecnoblade

[@RealMikeDobbs]

Huh- yeah I can hear it 🤣

[@kiyoshinguyen6213]

@@RealMikeDobbs Wait You Know TecnoBlade The Minecraft Player?

[@RealMikeDobbs]

Well I do now 🤣 I googled him after your comment- watched the hide and seek video with the fridge prize- very entertaining 👍

[@brendat4387]

thank you so much

[@RealMikeDobbs]

You're very welcome 😄

[@MamaMarong-u6c]

Thanks sir

[@RealMikeDobbs]

You're very welcome 😄

[@OkeDavidDamilola]

Thanks so much

[@RealMikeDobbs]

You’re very welcome 😀