CIE Mathematics 9709 (P1) past exam question trigonometry help please!
Hi,
I have a past paper question that I don't understand the working for, even after having looked at the mark scheme. Please see question attached.
I'm actually getting half of it right, it's just the other half that I'm having trouble with...
Here's my working so far:
First I found length CE in terms of d, in order to add this value to my result for ED and thus find required length CD (this is the part I got right) - So length CE=
sin60°= opposite/ 2√3 d -->
√3/2 = opposite/ 2√3 d -->
opposite = 2√3 d x √3/2 = length CE
This is where I seem to go wrong - finding the length ED=
First I drew an additional line from B to D, thus making the BED section of the trapezium a triangle and solving ED using trigonometric values. Since angle BED=90°and 1/2 of angle ADE (which was 90°before triangle was drawn)=45°, angle DBE = 180-(45+90) = 45°
Before being able to find ED, I first found length BE to form one side of the new triangle:
opposite/adjacent = tan
tan60°= 2√3 d x √3/2 / adjacent
√3 = 2√3 d x √3/2 / adjacent Adjacent is BE -->
√3 BE = 2√3 d x √3/2 dividing both sides by √3-->
BE = 2d x √3/2
Now I solved for ED using this info...
tan45°= opposite/ 2d x √3/2
1 = opposite/ 2d x √3/2 --> Opposite is ED
opposite = 2d x √3/2 = length ED
Adding length CE =
2√3 d x √3/2 and
length ED = 2d x √3/2
should give answer of 4d if I did it correctly! But adding CE to ED does not, and I'm confused as to why??
The working in the mark scheme says:
2dsin30°+ 2√3 dsin60°=
2d x 1/2 + 2d√3 x √3/2 = 4d
The part of the answer in bold I seem to have correct? But I don't see how they used 2dsin30°when none of the values for this triangle is equal to the other required length... Even forming a triangle from A to E doesn't work, (with A being 15°), and the angle measures do not add up to 180°
Help ASAP would be appreciated! THANK YOU!!
I have a past paper question that I don't understand the working for, even after having looked at the mark scheme. Please see question attached.
I'm actually getting half of it right, it's just the other half that I'm having trouble with...
Here's my working so far:
First I found length CE in terms of d, in order to add this value to my result for ED and thus find required length CD (this is the part I got right) - So length CE=
sin60°= opposite/ 2√3 d -->
√3/2 = opposite/ 2√3 d -->
opposite = 2√3 d x √3/2 = length CE
This is where I seem to go wrong - finding the length ED=
First I drew an additional line from B to D, thus making the BED section of the trapezium a triangle and solving ED using trigonometric values. Since angle BED=90°and 1/2 of angle ADE (which was 90°before triangle was drawn)=45°, angle DBE = 180-(45+90) = 45°
Before being able to find ED, I first found length BE to form one side of the new triangle:
opposite/adjacent = tan
tan60°= 2√3 d x √3/2 / adjacent
√3 = 2√3 d x √3/2 / adjacent Adjacent is BE -->
√3 BE = 2√3 d x √3/2 dividing both sides by √3-->
BE = 2d x √3/2
Now I solved for ED using this info...
tan45°= opposite/ 2d x √3/2
1 = opposite/ 2d x √3/2 --> Opposite is ED
opposite = 2d x √3/2 = length ED
Adding length CE =
2√3 d x √3/2 and
length ED = 2d x √3/2
should give answer of 4d if I did it correctly! But adding CE to ED does not, and I'm confused as to why??
The working in the mark scheme says:
2dsin30°+ 2√3 dsin60°=
2d x 1/2 + 2d√3 x √3/2 = 4d
The part of the answer in bold I seem to have correct? But I don't see how they used 2dsin30°when none of the values for this triangle is equal to the other required length... Even forming a triangle from A to E doesn't work, (with A being 15°), and the angle measures do not add up to 180°
Help ASAP would be appreciated! THANK YOU!!
Drop a line vertically from B so that it cuts AD at a new point F and angle BFA is a right angle. Now BF / AD = sin 30. We know AD = 2d and sin 30 = 1/2, from which BF = AD sin 30 = 2d x 1/2 = d.
Now consider that BEDF is a rectangle. Therefore we can say that ED = BF = d.
Now consider that BEDF is a rectangle. Therefore we can say that ED = BF = d.
Great!!! Thank you so much!!!! That makes much more sense! Sorry to be a bother, but just wondering why the way I initially tried solving the problem didn't actually work (apart from the fact that it was much harder solving it that way)??
Thanks again.
Thank you so much!!!! That makes much more sense! Sorry to be a bother, but just wondering why the way I initially tried solving the problem didn't actually work (apart from the fact that it was much harder solving it that way)?? Thanks again.
Original post by She'llBeApples
Great!!! Thank you so much!!!! That makes much more sense! Sorry to be a bother, but just wondering why the way I initially tried solving the problem didn't actually work (apart from the fact that it was much harder solving it that way)??
Thanks again.
Thank you so much!!!! That makes much more sense! Sorry to be a bother, but just wondering why the way I initially tried solving the problem didn't actually work (apart from the fact that it was much harder solving it that way)?? Thanks again.
There is no justification for your 45 degree angles. (Now that you know the answer, you can easily work out the true value of angle DBE if interested).
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