## zhane2015 2 years ago What is the value of w? triangle (1 point) 7 3.5 7square root of three 14

1. zhane2015

|dw:1360703526596:dw|

2. Zelda

Take a look here and see if you can figure it out: See attached

3. Directrix

30-60-90 theorem in words.

4. zhane2015

Thank yoou soo much

5. zhane2015

@Directrix I'm sorry I thought I understood what I was doing but if you could just explain how to solve for w please, and @Zelda if you can help i would appreciate it

6. Directrix

First, you have to know what the 30-60-90 theorem says. It is written above in both symbols and words. Next, you have to know the names of the parts of the 30-60-90 triangle. I am marking them on a drawing. |dw:1360705600824:dw|

7. Directrix

Do you understand that so far?

8. Directrix

We will go step by step so that you understand. That is why I am asking.

9. zhane2015

yes

10. Directrix

If one angle of a right triangle is 30, then the other acute angle is 60. So, we have a 60 leg. Then, there is the hypotenuse. |dw:1360705782032:dw|

11. Directrix

Does that make sense? If so, we're about to break out the theorem. :)

12. zhane2015

Yes so far.

13. Directrix

That's good news. So far, so good.

14. Directrix

We want the length of w which is the hypotenuse. But, all we are given is the 60 leg.

15. zhane2015

Yes

16. Directrix

When fooling with the 30-60-90 theorem, get the 30-leg first. I know we are not asked for the 30-leg but the 30-leg is the key to finding w, the hypotenuse.

17. Directrix

Theorem Time; The 60-leg is sqrt(3) times the 30-leg. Agree?

18. zhane2015

Whoa, can you draw that??

19. Directrix

|dw:1360706227544:dw|

20. Directrix

|dw:1360706398553:dw|

21. Directrix

Questions? (We have one more step. We are not yet finished.)

22. zhane2015

I understand

23. Directrix

Note that in the latest posted picture, the 60 leg shows up as sqrt(3) times the 30-leg.

24. zhane2015

Yes, I am aware of that.

25. Directrix

The second part of the 30-60-90 theorem states that the hypotenuse is two times the 30-leg.

26. Directrix

|dw:1360706596069:dw|

27. zhane2015

Ok...

28. Directrix

So, w = 14. I can write it out. |dw:1360706716509:dw|

29. Directrix

|dw:1360706845397:dw|

30. Directrix

You can see the pattern in the diagram. That was what Zelda was talking about.

31. Directrix

Question?

32. zhane2015

No, and Thank You very much.

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