## anonymous 3 years ago So, on my right triangle triangle I have here, they give all the sides and are asking for an angle The sides are Opp=15 Adj=8 Hyp=17 And we are looking for the x angle.

1. anonymous

Do you know SOHCAHTOA? Your sine, cosine, and tangent laws?

2. anonymous

Yes

3. anonymous

Okay, since you know all three side lengths, you can use any of the three functions to determine x.

4. anonymous

For example, $$\sin x = \frac{\text{opp}}{\text{hyp}}$$

5. anonymous

And that is it? Just use 17 over 15 ,divide and my answer would be 1.13?

6. anonymous

It's not x = 1.13. It's sin x = 1.13.

7. anonymous

Ah, sorry for not using correct mathematical vocabulary.

8. anonymous

No, that's not my point. The point is, you need to solve for x. Right now, you only know sin x.

9. anonymous

You need to get rid of the sin.

10. anonymous

Oh? How is this done?

11. anonymous

One thing first. It's not 17/15, it's 15/17.

12. anonymous

Got it

13. anonymous

So, $$\sin x = \frac{15}{17} = 0.882$$

14. anonymous

To get rid of the sin, you calculate $$\sin^{-1}$$. On your calculator, you should have a way to do this.

15. anonymous

So, $$x = \sin^{-1} (\frac{15}{17})$$

16. anonymous

I did not know there was such an option? Thank you.

17. anonymous

You might need to hit something like 2nd function, or inverse, then hit sin.

18. anonymous

You should end up with something around 60 degrees, if it's sine of 15/17.

19. anonymous

This isn't my outcome, I get a decimal of 1.001

20. anonymous

Okay, so you took your amount (0.882) and hit inverse sine (sin^-1) and got 1.001?

21. anonymous

Oh but wait, that is sin(h), Sorry, personal mistake.

22. anonymous

No worries.

23. anonymous

Since you knew all the sides, you could have also done $$x = \cos^{-1} (\frac{8}{17})$$ or $$x = \tan^{-1} (\frac{15}{8})$$, and gotten identical answers.

24. anonymous

Odd, I get the decimal of 0.795, how does this lead to 60 degrees?

25. anonymous

What calculation gives you 0.795?

26. anonymous

Well, seeing as I'm using the computer based calculator, this may have swayed my calculation. When typed in, it shows up as *asinh(15 /17)*

27. anonymous

Where did you type that in?

28. anonymous

But lo, I have found my answer as you have predicted, thank you so much kind sir, It was simply a typing error.

29. anonymous
30. anonymous

Good stuff! You're very welcome. :)

31. anonymous

I shall be on my way! Good day to you, and thank you for your time.

32. anonymous

You too, David! Cheers!