## anonymous one year ago help please :)Students are building a trebuchet for their physics class. The model is shown below. If the length of DA measures 25 inches, then what to the nearest inch is the measure of the support AC?

1. anonymous

2. zepdrix

|dw:1441847743206:dw|

3. zepdrix

So just some trig stuff, ya? :)

4. anonymous

okay how would I figure this out?

5. zepdrix

In relation to our angle, we care about the side adjacent (next to it), and the side opposite the angle as well.

6. zepdrix

Which of your three trig functions makes use of adjacent and opposite? :)

7. anonymous

sine cosine tangent?

8. zepdrix

Yes, those three are the ones we're considering.$\rm \sin \theta=\frac{opposite}{hypotenuse},\qquad \cos \theta=\frac{adjacent}{hypotenuse},\qquad \tan \theta=\frac{opposite}{adjacent}$It looks like tangent is the one we want, ya? :D

9. anonymous

yes

10. zepdrix

$\large\rm \tan\theta=\frac{opposite}{adjacent}$So we need to plug in the angle and side lengths.$\large\rm \tan55^o=\frac{x}{25}$Understand how I was able to set that up? :o

11. anonymous

not really

12. zepdrix

|dw:1441848312912:dw|If our angle is located here in the upper left corner, then our side opposite the angle is over here.

13. anonymous

okay yea I do sorry that was so obvious lol

14. zepdrix

The side we're trying to solve for, I labeled x. So we need to isolate the x. It's being divided by 25. How can we undo that?

15. anonymous

Do we divide it by 3?

16. zepdrix

Sorry it didn't give me the notification D: We're dividing by 25, so let's multiply both sides by 25 to undo that :D

17. zepdrix

$\large\rm 25\cdot\tan55^o=\frac{x}{\cancel{25}}\cdot\cancel{25}$

18. anonymous

so I need to multiply 25*55?

19. zepdrix

No! Be careful not to do that! :) Maybe I should have put brackets around our 55 to be clear. He is the argument of your trig function, he is trapped inside of there. He can't come outside, and the 25 can't come inside. He's grounded :O

20. zepdrix

$\large\rm 25\cdot\color{orangered}{\tan(55)}=x$

21. zepdrix

You can probably put it into your calculator all at once like that! :) $$\large\rm 25\times\tan(55)$$ Make sure you're in degree mode!

22. anonymous

35?

23. zepdrix

Yay good job \c:/

24. zepdrix

Rounded closer to 36 I guess :) But whatever

25. anonymous

it wasn't an option but thank you I really didn't understand this but thank you so much for walking me through it. :)