Geometry Trouble: Solve triangle using technique in model

[Nessittere]

Guys, I'm stuck on such a task, so I sent my question to several mathematical forums but I have not received an answer yet, tell me how to solve my problem? Need urgent help!
Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle. Hypotenuse = 12
Long=?

 

[Dr.Peterson]

Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle. Hypotenuse = 12 View attachment 9299
Long=?

Please show us what you do understand about the problem (do you know the definitions of sine and cosine?), and where and why you are stuck. What is it that you are struggling to do? What is "the technique in the model above", which ought to give you the help you need?

 

[Nessittere]

Please show us what you do understand about the problem (do you know the definitions of sine and cosine?), and where and why you are stuck. What is it that you are struggling to do? What is "the technique in the model above", which ought to give you the help you need?

I realized that this is connected with Pythagorean theorem, and here we need to take formula а^2+b^2=c^2.
If hypotenuse=12.... 12^2=144 but I dont know how is short line and how I can calculate with angles and where I must put sine and cosine?

 

[Deleted member 4993]

I realized that this is connected with Pythagorean theorem, and here we need to take formula а^2+b^2=c^2.
If hypotenuse=12.... 12^2=144 but I dont know how is short line and how I can calculate with angles and where I must put sine and cosine?

From the diagram, do you see that:

\(\displaystyle sin(30°) \ = \dfrac{short}{hypotenuse}\) ?

Do you know the numerical value of sin(30°)?

 

[Dr.Peterson]

I realized that this is connected with Pythagorean theorem, and here we need to take formula а^2+b^2=c^2.
If hypotenuse=12.... 12^2=144 but I dont know how is short line and how I can calculate with angles and where I must put sine and cosine?

If you use sine and cosine, you don't need to use the Pythagorean theorem.

If you don't know about them, then you can instead recognize that the triangle is half of an equilateral triangle, and Pythagoras is useful then.

But this is why I asked you what you have learned, and what example you were given. Presumably they used one of these two methods; we can't know which until you tell us.

 

[Nessittere]

Thank you very much for your answers, you really helped!

 

[stapel]

Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle. Hypotenuse = 12

View attachment 9299

Long=?

All I'm seeing is a right triangle with the three sides labelled. I'm not seeing any "technique" or "model". Can you tell us what the "model"/"technique" actually is? Thank you!