## ASpasaro 3 years ago Look at the triangle. A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x°. The side adjacent to the acute angle has length 15 centimeters and the side opposite to the acute angle has length 8 centimeters. What is the value of cos x°? Can someone Explain to me how to solve cos I know it is adj/hyp

1. Freyes

|dw:1353205436011:dw|

2. Freyes

|dw:1353205487282:dw|

3. Freyes

Solving for x.. you would do inverse cosine on the two sides to get the angle in between the two. $x = \cos^{-1} (15/17)$

4. ASpasaro

Why would I inverse cos. I also have the other leg which length is 8.

5. satellite73

you don't need the angle unless you are asked for it

6. ASpasaro

They are asking for the angle

7. ASpasaro

would it be 8 over 17 = x over 15

8. tcarroll010

If you need the angle and not just cos of the angle, then freyes gave you a good answer. The angle is determined by the inverse trig functions. His equation gives the angle.

9. ASpasaro

Does it matter which side is used for adj then?

10. jazy

|dw:1353206463570:dw| You want to solve for cos(x) and you already did. The answer if 15/17

11. jazy

*is

12. jazy

15 ÷ 17

13. tcarroll010

You would use 15/17 for the cos. You could use 8/17 for the sine. Either one (and otherways, too) will give the answer, but one is for cos, the other is for sine.

14. tcarroll010

8/17 would have to be for sine because 8 is the opposite, not adjacent side.

15. ASpasaro

16. tcarroll010

Yes, that's a good diagram to use. One other thing, you have to set your calculator for whether you want degrees or radians for the angle. And again, do you want the angle or just cos of the angle? Or both?

17. ASpasaro

18. ASpasaro

I am so to confused im sorry if I am asking a lot of questions.

19. tcarroll010

Actually, adjacent is "right next to" the little arc. It's "close by" or "right to the side". "8" is opposite, not adjacent. And don't worry about your questions, they're all good, and that's how you learn. You're doing fine.

20. tcarroll010

A good way to remember adjacent is that it shares a point with the hypotenuse that is right where the angle in question is. The angle is nestled in where the adjacent and hypotenuse meet.

21. jazy

It depends which angle you are looking for. Adjacent is between the right angle and the other given angle, in this case, x. |dw:1353207247146:dw|

22. ASpasaro

Then wouldnt they both be adj technicaly

23. tcarroll010

They are adjacent depending on what angle you are looking at. If you had an angle y at the top tip, then "8" would the adjacent side for THAT angle.

24. ASpasaro

Oh okay. I gotchya

25. tcarroll010

It's wonderful when we get "aha" moments! You just learned and consolidated that learning. Well done!

26. ASpasaro

Thank you

27. tcarroll010

You are quite welcome!