## highschoolmom2010 2 years ago Find the values of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.

1. highschoolmom2010

2. katherine.ok

you have multiple ways. one is to recognize that this is isoceles triangle ( the triangle shape with two equal sides)

3. highschoolmom2010

i saw that to begin with

4. katherine.ok

which makes the right triangle have internal sum of 90+ 42+w= 180.

5. katherine.ok

or does w mean the height?

6. highschoolmom2010

i believe w is height

7. highschoolmom2010

im not entirely sure

8. katherine.ok

then sin42= w/102

9. katherine.ok

and cos 42= (2/x)/102

10. katherine.ok

cos42= (x/2)/102****

11. highschoolmom2010

$(102)*\sin 42=\frac{ w }{ 102 }*102$ $102 \sin 42=w$ w$\approx 68$

12. highschoolmom2010

so how now that i have found w how do i get x?

13. katherine.ok

cos42= (x/2)/102

14. satellite73

pythagoras

15. satellite73

half of $$x$$ is $$\sqrt{102^2-68^2}$$

16. highschoolmom2010

can i have a fraction in the numerator

17. satellite73

so $$x=2\sqrt{102^2-68^2}$$

18. satellite73
19. jdoe0001

@highschoolmom2010 you can always just use the cosine of 42 degrees you know don't spare functions with your SOH CAH TOA

20. katherine.ok

Satelite using wolfram alpha. LOL hes definitely not highschool student.

21. katherine.ok

cos42=x/204= (x/2)/102 (the one i typed few mins ago)

22. highschoolmom2010

^^confused -_-

23. highschoolmom2010

@ganeshie8 any help

24. jdoe0001

$$\bf sin(42^o) = \cfrac{\textit{opposite side}}{\textrm{hypotenuse}} \implies \cfrac{w}{102} \implies \color{blue}{sin(42^o) \times 102} = w\\ cos(42^o) = \cfrac{\textit{adjacent side}}{\textrm{hypotenuse}} \implies \cfrac{\textit{half of "x"}}{102} \implies \color{green}{cos(42^o) \times 102} = \textit{half of "x"}$$

25. highschoolmom2010

$\cos (42)\rightarrow 65*102$

26. jdoe0001

well, if "half of x" = 65, yes

27. highschoolmom2010

ive done confused myself again

28. jdoe0001

then again, if you already know that x= 65 * 2, you don't have to do the cosine part :)

29. highschoolmom2010

aw heck imma use @satellite73 s method

30. highschoolmom2010

$\sqrt{108^2+68^2}=108-68=40$ $\sqrt{40}=2\sqrt{10}$

31. highschoolmom2010

but that doesnt look right

32. jdoe0001

using the cosine, I get ahemm, something else for "x"

33. highschoolmom2010

i dont understand now to use it with this problem

34. highschoolmom2010

for x

35. katherine.ok

okay wild katherine has appeared.

36. highschoolmom2010

|dw:1376262142492:dw|

37. katherine.ok

cos42=x/204

38. highschoolmom2010

:( math is really hard for me right now yall

39. katherine.ok

x=204*cos42.

40. highschoolmom2010

ya know that makes it a whole lot easier

41. katherine.ok

now the number should be above 150, which is so much more amazing than just sqrt(40).

42. highschoolmom2010

151.6

43. highschoolmom2010

ty @katherine.ok @satellite73 @jdoe0001