hi all, this is q18 p247 in the cambridge book if you have it. im really stuck - ive tried several different methods but nothin worked to match the answer in the book.
This question has 4 parts - but Im having problems with one that doesnt have
much to do with series.
The area available for planting in a particular paddock of a vineyard measures
100m by 75m. In order to make best use of the sun, the vines are planted in
rows diagonnaly across the paddock, with a 3m gap between adjacent rows. (this
gap is the perpendicular distance between rows).
a) What is the length of the diagonal of the field?
b) What is the length of each row on either side of the diagonal?
What I did:
FOr part a) i used pythagoras's theorem and got 125m which was correct. However
I'm having trouble with part b. I found the ration of the triangle 75:100:125
reduces to 3:4:5 which I vaguely remember is the perfect triangle ratio or
something. This is hard to explain without a diagram, but I made another
triangle by drawing a line from where the line next to the diagonal met the side
of the field to the meet the diagonal perpendicularly. This line was 3m from
the info in the question. I then found that this small triangle was similar to
the 3:4:5 triangle by equating the angles. Because the sides must be in the
same ratio, I found that the sides of the smaller triangle had to be 3m, 2.25m
and 3.75m. SInce the 3.75m side was on the field's border, i used pythagoras
again to find the length of the line next to the diagonal by: (75-3.75)^2 +
(100-3.75)^2 and then square rooting that. But I got 119.7... Since the answer
in the book is 118.75 I am really confused and not sure what else to try.
Hopefully you managed to understand all that, thanks for your help.
i just drew a quick diagram in paint to make it easier...
This question has 4 parts - but Im having problems with one that doesnt have
much to do with series.
The area available for planting in a particular paddock of a vineyard measures
100m by 75m. In order to make best use of the sun, the vines are planted in
rows diagonnaly across the paddock, with a 3m gap between adjacent rows. (this
gap is the perpendicular distance between rows).
a) What is the length of the diagonal of the field?
b) What is the length of each row on either side of the diagonal?
What I did:
FOr part a) i used pythagoras's theorem and got 125m which was correct. However
I'm having trouble with part b. I found the ration of the triangle 75:100:125
reduces to 3:4:5 which I vaguely remember is the perfect triangle ratio or
something. This is hard to explain without a diagram, but I made another
triangle by drawing a line from where the line next to the diagonal met the side
of the field to the meet the diagonal perpendicularly. This line was 3m from
the info in the question. I then found that this small triangle was similar to
the 3:4:5 triangle by equating the angles. Because the sides must be in the
same ratio, I found that the sides of the smaller triangle had to be 3m, 2.25m
and 3.75m. SInce the 3.75m side was on the field's border, i used pythagoras
again to find the length of the line next to the diagonal by: (75-3.75)^2 +
(100-3.75)^2 and then square rooting that. But I got 119.7... Since the answer
in the book is 118.75 I am really confused and not sure what else to try.
Hopefully you managed to understand all that, thanks for your help.
i just drew a quick diagram in paint to make it easier...
if anyone needs to know pm me.