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Trig q help

Hi I’ve found BQ but not sure how to get a side in triangle BCP
image.jpg504.5KB
Original post by e1eanor
Hi I’ve found BQ but not sure how to get a side in triangle BCP

Personally the quickest that I see is just using cosine rule then trig
You have BQ so you have an angle and a side of triangle BPQ. Therefore you can use trigonometry to find BP
You have two sides of the triangle BAQ so can use trigonometry to find angle QBA
This will help you find angle CBP (as CBA is a right angle)
You now have an angle and a side of BPC,,.from which you can use trigonometry once again to find BC
Hope that helps 🙂
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mqb2766
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Original post by e1eanor
Hi I’ve found BQ but not sure how to get a side in triangle BCP

If you have BC, then you have QP as its 30-60-90
then get QD as ABQ is similar to QPD.
So QD+6
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Original post by mqb2766
If you have BC, then you have QP as its 30-60-90
then get QD as ABQ is similar to QPD.
So QD+6

Thanks a lot have got it, can I ask about a polynomial division q?
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Original post by e1eanor
Thanks a lot have got it, can I ask about a polynomial division q?

sure
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Original post by mqb2766
sure

image.jpg Think I’ve gone wrong using the discriminant (to prove the equation has only one root)
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mqb2766
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The divison seems ok. You could verify by just multiplying the quadratic and linear terms and see if you get the cubic.

The quadratic has no roots if the discrimant is less than zero.
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Original post by mqb2766
The divison seems ok. You could verify by just multiplying the quadratic and linear terms and see if you get the cubic.

The quadratic has no roots if the discrimant is less than zero.

Thanks, I got -47 which <0 but the question said show it only has one root
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Original post by e1eanor
Thanks, I got -47 which <0 but the question said show it only has one root

The cubic has only one root which is x=2?
Original post by e1eanor
Thanks, I got -47 which <0 but the question said show it only has one root


You have shown the discriminant is less than 0 so the quadratic has no roots. The one root comes from the bracket (x-2).
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Original post by mqb2766
The cubic has only one root which is x=2?

Ah okay so I state -47<0 to show it has only one root (2) ?
Original post by e1eanor
Ah okay so I state -47<0 to show it has only one root (2) ?

Something like that.

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