Trigonometry question

[Attempt989]

Hi,
First time using this so hopefully I have posted correctly.

I cannot do the above question for the life of me I even checked the back of the book and cannot get the to the answer.

Many thanks in advance,

 

[Deleted member 4993]

View attachment 19889
Hi,
First time using this so hopefully I have posted correctly.

I cannot do the above question for the life of me I even checked the back of the book and cannot get the to the answer.

Many thanks in advance,

Have you made an approximate sketch of the problem?​

​

Did you label the chord, the center of the circle and the angle (subtended by the chord) at the center?​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Attempt989]

I have attached my calculation which are wrong. They haven’t gave me any diagram. I only have the question from the text. Hope my working outs help to find my error.

 

[Harry_the_cat]

Your first(and really bad) mistake is to take cos(30) when 30 is a length NOT an angle. When you calculate sin(x) or cos(x) or tan(x) the "x" needs to be an angle (at this stage anyway). The way to find the third side in a right angle triangle is Pythagoras' rule. I'm assuming you have learnt that.

Before I go on, there are a few ways to do this problem. I need to know if you have learnt the law of sines and the law of cosines. Or have you just learnt the ratios ie sin x = opp/hyp etc? What you have learnt will determine the best way to approach the problem.

 

[Attempt989]

Your first(and really bad) mistake is to take cos(30) when 30 is a length NOT an angle. When you calculate sin(x) or cos(x) or tan(x) the "x" needs to be an angle (at this stage anyway). The way to find the third side in a right angle triangle is Pythagoras' rule. I'm assuming you have learnt that.

Before I go on, there are a few ways to do this problem. I need to know if you have learnt the law of sines and the law of cosines. Or have you just learnt the ratios ie sin x = opp/hyp etc? What you have learnt will determine the best way to approach the problem.

Hi,
Firstly, thank you for the help I can’t believe I made that mistake with the cos(30)

For now I only know ratios but the laws are on my syllabus. So maybe the ratio way is best for now.

I have attached as far as I am getting with the fixed cos(30)

 

[Harry_the_cat]

Ok so now double the angle you've found. That's the angle at the centre. Then find sin and cos of that angle.
BTW, there is a better way of answering this question but you need a bit more trig in your toolbox.

 

[Attempt989]

Very grateful for your help. I will look forward to learning the better way as I progress. For now I’m just glad this one is done. Thanks again