## Falling_In_Katt one year ago <RST is an equilateral triangle; TX and RS. If TX = 6 then RX =

1. mathstudent55

You mean triangle RST is equilateral?

2. Falling_In_Katt

yes

3. mathstudent55

Where is point X? Is there a figure?

4. Falling_In_Katt

5. Falling_In_Katt

there

6. mathstudent55

In the problem, you wrote "TX and RS." but you did not complete the sentence. What are we supposed to know about TX and RS?

7. Falling_In_Katt

they are perpendicular

8. mathstudent55

Ok.

9. mathstudent55

We are looking for a. |dw:1435246962181:dw|

10. mathstudent55

Have you learned about the ratios of the length of the sides of 30-60-90 triangles?

11. Falling_In_Katt

no

12. mathstudent55

An equilateral triangle is also equiangular, so all angles measure 60 degrees. |dw:1435247132947:dw|

13. mathstudent55

Because of symmetry, the top angles are 30 degrees each |dw:1435247199089:dw|

14. mathstudent55

Triangle RTX is a 30-60-90 triangle. The ratio of the lengths of the sides of a 30-60-90 triangle is: $$1~:~ \sqrt 3~:~ 2$$

15. mathstudent55

The ratio of the lengths of the legs is $$1 ~:~ \sqrt 3$$ The long leg is $$\sqrt 3$$ times longer than the short leg.

16. Falling_In_Katt

My brain is not understanding this.