Maybe someone can help me solve this task, I really need help, please reply

[tato1982]

Please help me

[exchemist]

1 hour ago, tato1982 said:

Please help me

Sine rule?

[tato1982]

1 hour ago, exchemist said:

Sine rule?

Please help me

I could not get an answer and maybe you can help me. No such a simple taskI could not get an answer and maybe you can help me. No such a simple task

1 hour ago, exchemist said:

Sine rule?

I could not get an answer and maybe you can help me. No such a simple task

[swansont]

Angles of a triangle add to 180.

Angles at D are on a line, so they add to 180

That gives 4 equations with 4 unknowns

 

[tato1982]

2 hours ago, exchemist said:

Sine rule?

Can you write me the equation ?? Please write me

Can you write me the equation ?? Please write me

Please writhe me

[exchemist]

1 minute ago, tato1982 said:

Can you write me the equation ?? Please write me

Can you write me the equation ?? Please write me

Please writhe me

No. You've been given 2 ideas on what to do so now you need to show some initiative. We don't just give answers here, because that does not help people learn. 

[tato1982]

I do not know English well. I can not even understand what the equations are talking about. I used the sine theorem, I can not solve it completely and I wonder how you explain it.

[exchemist]

10 minutes ago, tato1982 said:

I do not know English well. I can not even understand what the equations are talking about. I used the sine theorem, I can not solve it completely and I wonder how you explain it.

Don't forget you can apply the Sine Rule to the big triangle as well as to the 2 smaller ones. So, for example, you can make ratios of Sin 48deg with TV as well as with TD.

[tato1982]

Yes, I did that, with the sine theorem, but in the end I can not solve it. Here I accept it

[Genady]

I think this problem can be solved by geometrical constructions rather than generically using sine rule, because the numbers, 48 and 18 degrees, have a specific property: on one hand, 48+18=66, on the other hand, 180-48=132=66x2 could be two angles of 66 degrees of an isosceles triangle with one angle of 48 degrees.

[swansont]

Triangle STD:  angle STD + TDS + TSD = 180

TSD is given as 48º

There are two other triangles which you should be able to write down, and you have TDS + TDV = 180

The rest is algebra, which you need to be able to do, and no, nobody is going to do it for you.

 

[studiot]

14 hours ago, Genady said:

I think this problem can be solved by geometrical constructions rather than generically using sine rule, because the numbers, 48 and 18 degrees, have a specific property: on one hand, 48+18=66, on the other hand, 180-48=132=66x2 could be two angles of 66 degrees of an isosceles triangle with one angle of 48 degrees.

Yes, +1

By direct drawing, (ie construction) I very quickly made the result about 10^o last night.

22 hours ago, swansont said:

Angles of a triangle add to 180.

Angles at D are on a line, so they add to 180

That gives 4 equations with 4 unknowns

 

Sadly this is not enough.

As can be seen from my sketch the four angle equations alone are not independent so there are infinitely many solutions, corresponding to the infinite many positions we may place D between S and V.

The problem is, however, solvable using the extra information that ST = DV.

The fact that we do not need to know its actual length shows that we are not in the ambiguous sine rule case and that the problem is solvable without knowing this length.

Genady's constructive solution using isoceles triangles is creative.

[tato1982]

Okey

16 hours ago, Genady said:

I think this problem can be solved by geometrical constructions rather than generically using sine rule, because the numbers, 48 and 18 degrees, have a specific property: on one hand, 48+18=66, on the other hand, 180-48=132=66x2 could be two angles of 66 degrees of an isosceles triangle with one angle of 48 degrees.

This is a good option, but how to build a magician's drawing is interesting

[studiot]

1 hour ago, tato1982 said:

Okey

This is a good option, but how to build a magician's drawing is interesting

There's no magic in it.

Have you abandoned an analytical solution ?

As swansont has told you I cannot do your work for you, but I see that you have been trying, even though you have not posted your complete efforts.

It is always a good idea to post these as we can then see where you are either stuck or have gone wrong.

 

So here are some analytical hints.

 

1) Look at triangles SDT and DVT and write out the sine rule for each.

2) Note that DT is common to both these triangles so by comparing (equating) expressions for this common side you can obtain one equation.
I obtained one involving the angle  have labelled A, the angle you have labelled X and the angle 18.

3) Now look at A, X and 18 from a geometric point of view. They have a geometric relationship in triangle DTV

4) This gives you two equations in 2 unknowns to solve.

 

Let us know how you get on.

[tato1982]

Draw the sections CS from point B to point C and point C from point B so that the angle BS = CS and the angle SBC = SCB = 66 then how to proceed help me.

[studiot]

5 hours ago, tato1982 said:

Draw the sections CS from point B to point C and point C from point B so that the angle BS = CS and the angle SBC = SCB = 66 then how to proceed help me.

So SB = SC

and

KC = KS

But how does that help you ?

And why have you relabelled your diagram ?

Perhaps @Genady  will help you.

 

Have you tried doing what I suggested ?

It is a nice little problem.

[tato1982]

The trigonometric solution was good, thank you for the help. But I was wondering if there was another solution. How to draw another option, give me a hint of a 66-degree equilateral triangle

If there is another way folks I wonder how to solve this task without trigonometry

[Genady]

Unfortunately, in spite of noticing that angles' "conspiracy", I don't see how to use it in a drawing /construction.

On the other hand, the "analytical hints" from @studiot's post above lead to the solution quite directly.

[tato1982]

I do not know how to draw a picture, if someone can bet, maybe we can not do anything

[studiot]

On 2/24/2022 at 1:49 PM, studiot said:

By direct drawing, (ie construction) I very quickly made the result about 10^o last night.

When I said this I did not construct auxiliary triangles.
I did try dropping perpendiculars from T, etc,  but very quickly came to the conclusion that this would work but actually involve more work as you do not know the actual length of ST and DV.
Therfore this length must cancel out and there are no geometrical theorems where this happens so trigonometric formulae must be involved for calculation.

However since the actual length if ST does not matter, the result must be true for any length of ST < SV.

So I just chose 3 quite different lengths and drew the figure based on these three quick sketches.
Then I measured X in each case and confirmed that it was the same angle.

Edited February 26, 2022 by studiot

[tato1982]

Your opinion is clear. That is, without trigonometry we will not find another way.

[studiot]

14 minutes ago, tato1982 said:

Your opinion is clear. That is, without trigonometry we will not find another way.

Only by direct measurement with a protractor or other measuring equipment.

[Genady]

Let's try "reverse engineering". The trigonometric solution gives an exact angle, x=12 degrees. It still seems to hint to a geometric solution.

Here is another "conspiracy": 12+18=30, 48-18=30.

Any new ideas?

[tato1982]

It's a good idea but I could not think of how to draw it

[studiot]

6 minutes ago, Genady said:

Let's try "reverse engineering". The trigonometric solution gives an exact angle, x=12 degrees. It still seems to hint to a geometric solution.

Here is another "conspiracy": 12+18=30, 48-18=30.

Any new ideas?

You have to use a formula that connects angles and lengths.

Isoceles/equilateral triangles are the only ones that do this.