## highschoolmom2010 Group Title Find the value of each variable. If your answer is not an integer, express it in simplest radical form 11 months ago 11 months ago

1. highschoolmom2010 Group Title

2. Psymon Group Title

Do you know your trig functions? Like what sin, cos, tan are in regards to a triangle?

3. highschoolmom2010 Group Title

nope not really

4. Psymon Group Title

Ah. Alright, hang on then :P Keep in mind as I write these out, they are all in reference to the angle you are using.

5. highschoolmom2010 Group Title

that helps alot :DD

6. Psymon Group Title

$\sin = \frac{ opposite side }{ hypotenuse }$ $\cos = \frac{ adjacent side }{ hypotenuse }$ $\tan = \frac{ opposite side }{ adjacent side }$ People are ususally taught Soh Cah Toa as a way to remember which sides the trig functions refer to. Now again, these are in reference to your angle, so I'll draw that real quick.

7. Psymon Group Title

|dw:1375810320869:dw|

8. Psymon Group Title

|dw:1375810420360:dw|

9. Psymon Group Title

That kind of make sense so far?

10. highschoolmom2010 Group Title

so far yes

11. Psymon Group Title

Okay, cool. So this is your triangle that we have then: |dw:1375810542321:dw|

12. Psymon Group Title

In order to solve this, we need to choose an angle (not the right angle) and then an appropriate trig function, sin, cos, or tan. The one we choose must include the side we know, 10 in this case, and then the value we want to find. that make sense?

13. highschoolmom2010 Group Title

im not entirely sure how to use them though

14. Psymon Group Title

Right, we're getting to that :P I just wanted to see if you were following me so far.

15. highschoolmom2010 Group Title

oh well yes im following ya

16. Psymon Group Title

Okay, cool. So next part: Let's say to find x I choose the 60 degree angle. Now in reference to the 60 degree angle, x is on the adjacent side of it. The value we know is the hypotenuse. Now remember, in reference to the angle we use, we want to choose either sin, cos, or tan. The one we choose now needs to include the adjacent side and the hypotenuse |dw:1375811355268:dw|

17. Psymon Group Title

So which one of the 3, sin, cos, or tan has adjacent and hypotenuse?

18. highschoolmom2010 Group Title

@Psymon cos?

19. Zale101 Group Title

cos = adjacent/hypotenuse so i think @psymon meant that

20. highschoolmom2010 Group Title

ive never used them so idk im used to using 30-60-90

21. Zale101 Group Title

that's correct, because your triangle has 60, and we can predict the other angle is 90. And, 90+60+30=180

22. jdoe0001 Group Title

in the 30-60-90 rule the hypotenuse is TWICE as long as the SHORTEST side the "other side" is the SHORTEST side times $$\bf \sqrt{3}$$

23. highschoolmom2010 Group Title

ok so how do i do this problem

24. jdoe0001 Group Title

is really pretty much handed out in a silver plate, with cake and ice cream really

25. mathstudent55 Group Title

In a 30-60-90 triangle, the three sides of the right triangle are in the ratio of: $$1 : \sqrt{3} : 2$$ That means that the shorter leg is 1/2 the length of the hypotenuse. The long leg is $$\sqrt{3}$$ times the length of the short leg.

26. jdoe0001 Group Title

if "the hypotenuse is TWICE as long as the SHORTEST side" what do you think is the length of the shortest side?

27. mathstudent55 Group Title

Here the hypotenuse is 10. The short leg is x. From the statement "the short leg is half the length of the hyopotenuse", what can you conclude about x?

28. highschoolmom2010 Group Title

|dw:1375817625354:dw|

29. highschoolmom2010 Group Title

short leg is 5 :DD

30. jdoe0001 Group Title

so there, shortest leg is 5 and the "other leg" is THAT MUCH $$\bf \Large \times \sqrt{3}$$

31. mathstudent55 Group Title

Great. That is correct, the short leg, x = 5. The long leg, y, is $$\sqrt{3}$$ times longer than the short leg. $$y = \sqrt{3} \times 5$$ What is y

32. highschoolmom2010 Group Title

so $5\sqrt{3}$

33. highschoolmom2010 Group Title

@mathstudent55 @jdoe0001

34. jdoe0001 Group Title

yes

35. highschoolmom2010 Group Title

was that all i need to do???

36. jdoe0001 Group Title

yeap

37. mathstudent55 Group Title

correct $$x = 5$$ $$y = 5\sqrt{3}$$ That is it

38. highschoolmom2010 Group Title

horray thanks @mathstudent55 & @jdoe0001 & @Psmon @Zale101

39. highschoolmom2010 Group Title

wish i could give everyone a medal