## highschoolmom2010 3 years ago Find the value of each variable. If your answer is not an integer, express it in simplest radical form **check answer**

1. anonymous

Um... missing something?

2. jdoe0001

should we get popcorn while you type in the variables?

3. highschoolmom2010

yall patience is a virtue

4. jdoe0001

SOH CAH TOA

5. jdoe0001

sounds like the tune of a hawaiian song, but that's all you need http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png

6. jdoe0001

hmmm well, I see, you're using the 30-60-90 rule

7. jdoe0001

well, hmm, still the 30-60-90 rule wouldn't end up using the sine function anyhow I mean you're given an angle's value, 30 degrees so I gather you're expected to use sine and cosine for that

8. jdoe0001

9. jdoe0001

hmm maybe not ...

10. jdoe0001

in a 30-60-90 rule the smallest side, will half the longest that is "x" the smallest, is half 40 the longest and the OTHER side, is $$\bf \sqrt{3} \times \text{smallest side}$$

11. jdoe0001

|dw:1375644053298:dw|

12. jdoe0001

45-45-90 assumes you have 2 angles of 45 degrees you have there one of 30, and is a right triangle, so you have another of 90 and lastly one of 60

13. jdoe0001

but yes, for the 45-45-90 rule, 2 sides are equal and the longest is $$\bf \sqrt{2}$$ of either side

14. jdoe0001

well, for that you'd need to use the $$\bf \sqrt{3}$$ ratio for the longer side

15. jdoe0001

|dw:1375644727216:dw|

16. jdoe0001
17. jdoe0001

those are the ratio relationships on a triangle with 30-60-90 angles if I were to stand up yours, it'd look like |dw:1375645193671:dw|

18. jdoe0001

so, what part confuses? in a 30-60-90 rule, each side have a ratio relationship, as shown above

19. jdoe0001

ok

20. jdoe0001

so you want to know what "x" is in the triangle notice that the triangle has a hypotenuse of 40 and 2 angles, a 30 degrees one and a 90 degrees one the other internal angle has to be a 60 degrees one so that makes it a 30-60-90 triangle, whose side relationships are well known

21. highschoolmom2010

i reposted it that way we wouldnt have all the ^^ in the way