## highschoolmom2010 2 years ago find the measure of < x using trigonometric ratios

1. highschoolmom2010

2. highschoolmom2010

@ganeshie8 IM HORRIBLE AT THESE

3. ganeshie8

we'll handle this the same way... SOH-CAH-TOA go to the angle corner, and figure out given sides as opposite,adjacent and hyp

4. agent0smith

Use tangent here. Tanx = opposite/adjacent. What side is opposite angle x? |dw:1376249499008:dw| $\Large \tan x = \frac{ \text{opposite} }{\text{adjacent} }$

5. highschoolmom2010

opposite of <x 8 adjacent to <x 5 hypotenuse unknown

6. agent0smith

Hypotenuse we don't need, use tanx = opp/adj.

7. highschoolmom2010

i know i like to list what i know :DD

8. agent0smith

Okay :)

9. agent0smith

That's a good tactic, especially for subjects like physics :)

10. highschoolmom2010

$\tan(x)=\frac{ 8 }{ 5 }$ $(5)*\tan x=\frac{ 8 }{ 5 }*(5)$

11. highschoolmom2010

like that ?

12. ganeshie8

nopes ! leave it as it is tanx = 8/5

13. ganeshie8

yes ! just divide the right side, then take inverse tan both sides

14. highschoolmom2010

i am used to having to to that i suppose

15. ganeshie8

haha i bet you're !

16. agent0smith

No need for extra work here :P $\tan(x)=\frac{ 8 }{ 5 }$ so $x = \tan^{-1} \frac{ 8 }{ 5 }$which you need a calculator for.

17. highschoolmom2010

x$\approx 58$

18. agent0smith

19. ganeshie8

right right !

20. ganeshie8

gw !!

21. highschoolmom2010

so when finding angles like ^^ use tan^-1

22. ganeshie8

see, you have tan x = 8/5

23. ganeshie8

you want to find x, so to find x you have to isolate x

24. agent0smith

tan^-1 is the "opposite" of tan, so you use it to undo it. Just like a square root is the opposite of squared, a square root undoes the squard.

25. ganeshie8

take tan^-1 both sides :- tan x = 8/5 tan^-1 tan x = tan^-1 8/5 x = tan^-1 8/5

26. highschoolmom2010

oh ok that makes sense :D

27. ganeshie8

left side, tan^-1 and tan cancel out

28. highschoolmom2010

TY soo much @agent0smith && @ganeshie8

29. ganeshie8

np :)

30. agent0smith

If you have sinx = some number, then you'd use sin^-1(some number) to undo it. Same for cosx = some number. But make sure you isolate the sinx or cosx, so it's like sinx = ... or cosx = ... ie you can't just do cos^-1 of 10cosx = 5, you'd have to divide by 10 first.