how do I know what tan60 is

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Polonium 84

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the problem being is how do i find out tan60 by itself without a calculator and no diagram?
 
Im not asking for a direct answer how do i figure out trig function roots without a calculator.
 
Polonium 84 said:
the problem being is how do i find out tan60 by itself without a calculator and no diagram?
Click to expand...

All you need to remember are these two triangles, and you don't even need to remember the surds in red because you can get them using the other two sides (by Pythagoras)...
trig.png
...and you'll also need to know "soh cah toa".

That's really just remembering the two numbers "1" and "1" for a 45° right triangle, and the two numbers "1" and "2 on the hypotenuse" for a 30° (and 60°) right triangle. Try looking at the triangles, cover them up and then redraw them from memory. Repeat until you remember them correctly. Good luck!

The above triangles are extracted from this post (click).
 
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Polonium 84 said:
View attachment 34132
the problem being is how do i find out tan60 by itself without a calculator and no diagram?
Click to expand...
Dear @Polonium 84,

On Thursday you posted a question (How do I do this without a calculator) and I, along with others, provided you with all the information you required to deal with the problem you posted.
However, you did not subsequently bother to post anything that showed you had managed to solve the problem originally posed by you.

It is just common courtesy for any new member posting a problem in this forum to respond, after they have been given appropriate help from the long-term members, by posting their own solution to their question or, at the very least, their attempt at solving it so that confirmation it's correct or further advice may be offered as appropriate.

When you posted that previous question (referred to above) I gave you the ‘benefit of the doubt’ (despite others’ concerns) regarding your knowledge of “Exact Values” because you quoted a couple of them in your question even though you appeared to (inadvertently?) misname one of them as “tan (30°)” rather than “cos (30°)”!

Now, just three days later, you are posting another question that shows that you have not taken on board the advice you were given in response to your previous question!
If you had learned the principles & theory that you were directed to in response to that previous post then you would have had no need to post this one as you would have acquired all the knowledge necessary to deal with your latest query.

The “tutors” in this forum are good enough to spend their time and energy looking at new members' problems, gauging (usually with very scant background information) what level of mathematical knowledge the OP (Original Poster) possesses and then judging what help would best help them solve their problem and in what format that help should be offered.
Those forum members all know how to solve the problems posed, most having many years’ experience in teaching Mathematics or using it in their own careers. However, their (laudable) aim is not to simply solve these problems for you but to help you to know how to solve them yourself!

If you are not prepared to put in the effort to learn the basic Mathematical principles needed to address your problem(s) then the help that can/will be offered to you in here is not just a waste of your time but also (more importantly) that of those who seek to help you. Please do not waste our time and efforts so cavalierly!

Your latest post suggests (to me) that you didn’t bother to read through (and adopt) all the advice that was offered to you in your previous one (or you wouldn’t have needed to post this question!). The fact that you are posting these questions further suggests (to me) that you are a student who is expected to have learned the Maths required to handle them. Alternatively, maybe you have just 'come across' them somewhere and are seeking to improve you knowledge of Maths but, in either case, I already directed you to the basic knowledge required to deal with them in my replies (qv) within the thread of your previous post.

However, despite having already provided all the help you need previously, I will lay it all out for you again and, this time, I trust you will make the effort to learn the information that you are being directed towards?

In my previous post I directed you to a single page on a website that gave you the basic Laws (Rules) for ‘handling’ square roots that were needed to solve the particular problem you posted and I further provided a simple example that succinctly illustrated their use. It seems, now, that you would benefit from learning everything that is provided on that site which has six pages in total.
I would therefore direct you to the (excellent) BBC site on “Surds” (here) and strongly suggest that you work your way through all six pages on that site (including attempting the ‘examples’ provided) so that you consolidate your knowledge of how to handle these entities.
This is the basic Mathematical knowledge required to deal with the kind of questions you are posting in the forum; if you are not prepared to make the effort to acquire and understand it then nobody in here can/will help you (short of just doing the work for you which, in essence, defeats the purpose of the forum) .

The other area of knowledge, that I (erroneously, it now appears) presumed you were already conversant with, is knowing or knowing how to derive the “Exact Values” of the Sine, Cosine & Tangent of 30, 45 & 60 degrees.

@Subhotosh Khan has already, very kindly, posted (above) a copy of my Worksheet on this issue but below (for your convenience) I am including a further copy of this Worksheet and I urge you to make your own copy of it and, this time, fill in all the blanks yourself.
You should retain a completed copy of this Worksheet in all your workbooks unless or until you are confident that you know all the results (or can derive them from the first principles provided in the worksheet) without further reference to it.

Once you have acquired all the Mathematical knowledge that you have been directed to in this post you should be in a position to answer (both) the questions you have posted in the forum recently and I’m sure everyone who has tried to help you would be interested to see your attempts at answering them.

Please, therefore, after studying the materials you’ve been directed towards, post (in the appropriate threads) your own attempts to answer your problems and, if they fail to reach a satisfactory conclusion, the more experienced forum members will be more than happy to provide further guidance on how the basic knowledge you have now gained (always assuming you have made that effort) may be used to reach a successful outcome.

Here, now, is the further copy of the worksheet referred to above. If you feel at all unable to complete it then I can only refer you to the basics of “Right-Angled Triangle Trigonometry” which I suspect everyone is presuming that you are already conversant with. (If not, then I am at a complete loss as to why you might have any interest in ‘tackling’ the kind of problems you are posting in the first place!)
Nevertheless, I also include my “Summary Sheet” on that Topic below the worksheet on Exact Values.

I trust that we will hear from you again (in the not too distant future?) with confirmation that you are now ‘expert’ in the topics of both “Surds” & “Exact Values”?

How to Derive the Exact Values of the Sine, Cosine & Tangent of 30, 45 & 60 degrees:
Exact-Values.png
​


Summary Sheet on Basic Right-Angled Triangle Trigonometry
Basic-R-A-Triangle-Trig.png


{img]https://i.ibb.co/jW5fvkx/Basic-R-A-Triangle-Trig.png[/img]
(For ease of replication should anyone wish to reproduce it. Just remember to replace the leading "{" with "[")

​
 
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One final piece of help:-

The question you have posted here looks like it has come from a website (or some “application”) where you are required to “Enter” your answers into the boxes provided and only the “correct” (expected) answers will be accepted.

If that’s the case, then in part c) the answer you first come up with may well not be accepted in the box(es).
I suspect (though I may be wrong, ofc) that the answer in the first box of part c) may need to be”3” though we will expect you to be able to demonstrate how that is arrived at.
 
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