## kennedav000 2 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. geoffb

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

2. kennedav000

Yes

3. geoffb

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

4. geoffb

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

5. kennedav000

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

6. geoffb

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

7. kennedav000

Ah, sorry for not using correct mathematical vocabulary.

8. geoffb

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

9. geoffb

You need to get rid of the sin.

10. kennedav000

Oh? How is this done?

11. geoffb

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

12. kennedav000

Got it

13. geoffb

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

14. geoffb

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

15. geoffb

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

16. kennedav000

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

17. geoffb

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

18. geoffb

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

19. kennedav000

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

20. geoffb

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

21. kennedav000

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

22. geoffb

No worries.

23. geoffb

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. kennedav000

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

25. geoffb

What calculation gives you 0.795?

26. kennedav000

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. geoffb

Where did you type that in?

28. kennedav000

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

29. geoffb
30. geoffb

Good stuff! You're very welcome. :)

31. kennedav000

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

32. geoffb

You too, David! Cheers!