Trig Question

[Mireya84]

Trying to figure what I missed on this question. Its worth 4 points. A friend said I rounded wrong; however the classmates I have asked - also got it wrong and not the full 4 points. Any tips?

 

[Deleted member 4993]

View attachment 14258
Trying to figure what I missed on this question. Its worth 4 points. A friend said I rounded wrong; however the classmates I have asked - also got it wrong and not the full 4 points. Any tips?

In this case, where 3 sides of a triangle is given and you are asked to calculate property of one angel, most of the time it is expedient to use laws of cosines:

36² = 15² + 39² - 2*15*39*cos(X) \(\displaystyle \ \to \ \) cos(X) = ? \(\displaystyle \ \to \ \) sin(X) = ?

 

[Harry_the_cat]

View attachment 14258
Trying to figure what I missed on this question. Its worth 4 points. A friend said I rounded wrong; however the classmates I have asked - also got it wrong and not the full 4 points. Any tips?

I don't know if angle Y is marked as a right angle or whether you have marked that in.
If it wasn't marked, you can't assume it is, but you can check using Pythagoras.
Does 15²+36² = 39²? Yes it does, so it IS a right angle. You can then use sin X = opp/hyp.
(Even if it is or isn't a right angled triangle, you could still use the law of cosines as Subhotosh has suggested.)
Note that the question asks you to find sin X not X.
Your first line is correct ie sin X = 36/39, now express this to the nearest hundredth as instructed.

 

[Deleted member 4993]

Does 15²+36² = 39²? Yes it does --- I was hoping OP will discover it while calculating through laws of cosines.