### Video Transcript

Jack is searching for treasure on
an island. He has the following map of the
island and has marked his location on it. Part a) In which direction should
Jack walk to get to the shipwreck? Circle your answer. Is it southwest, southeast,
northwest, or northeast?

There are also parts b), c), and d)
to this question, which we will look at later. We are told in the question that
north is pointing vertically upwards, which is usually the case when given a
map. The compass point south points
vertically downwards. West points to the left. And east points to the right
horizontally. The four main points on a compass
going clockwise from north are north, east, south, and west. One acronym that is used to
remember this is “Never Eat Shredded Wheat.”

The four answers in this part of
the question, southwest, southeast, northwest, and northeast, split these four
points. The compass point halfway between
north and east is northeast. Likewise, the compass point halfway
between south and east is southeast. We can find the compass points
southwest and northwest in the same way. We are told in this question that
Jack wants to walk to the shipwreck. The shipwreck is diagonally down
and to the left from Jack’s location. This corresponds to the compass
point southwest. The direction that Jack needs to
walk to get to the shipwreck is southwest. The second part of the question
says the following.

b) Circle the bearing of Dead Man’s
Cave from the Abandoned Fort. Is it 90 degrees, 180 degrees, 270
degrees, or 360 degrees?

Before starting this question, it
is important that we remember how we measure bearings. Bearings must always have three
figures. This is why there is a zero in
front of the 90 degrees. They are also measured clockwise
from north. We must use our protractor or
knowledge of compass points to measure in a clockwise direction from north. As we start to measure from north,
this compass point has the bearing 000 degrees. When we return to this compass
point having moved in a clockwise direction, we have completed a full circle. Therefore, this is also equal to
360 degrees.

The angle between the north and
east points on a compass is a right angle. As a right angle is equal to 90
degrees, the bearing when walking in an easterly direction is 090 degrees. The compass point south has a
bearing of 180 degrees. This is because north and south are
on a straight line. And angles on a straight line add
up to 180 degrees. Adding another 90 degrees to this
gives us 270 degrees. Therefore, when walking in a
westerly direction, we are travelling on a bearing of 270 degrees.

In this part of the question, we
want to calculate the bearing of Dead Man’s Cave from the Abandoned Fort. This means that we’re starting at
the Abandoned Fort and walking towards Dead Man’s Cave. Walking from the Abandoned Fort to
Dead Man’s Cave means we’re walking in a westerly direction. We know that when travelling west,
we’re travelling on a bearing of 270 degrees. This means that the correct answer
of the bearing of Dead Man’s Cave from the Abandoned Fort is 270 degrees.

We can show this on the map by
firstly drawing a north line at the Abandoned Fort as this is the point we are
starting from. We measure in a clockwise direction
until we hit the line that joins the Abandoned Fort and Dead Man’s Cave. This angle is equal to 270 degrees,
confirming that our answer is correct. A couple of common mistakes or
misconceptions here are that the angle would be 180 degrees as we’re walking in a
straight line. However, this is incorrect. We must always measure our bearings
from the compass point north in a clockwise direction. The third part of the question says
the following.

c) Find the distance, in metres,
from Jack’s location to Skull Rock.

When dealing with any question like
this on a map, it is important to note that we are finding the straight line
distance. This is sometimes called as the
crow flies. In reality, the distance that Jack
would have to travel might be greater as he might not be able to travel in a
straight line. And the ground might not be
flat. We are told underneath the map that
the scale is one centimetre to 400 metres. This means that one centimetre on
the map is equal to 400 metres on the island.

Our first step is to measure the
distance on the map between Jack’s location and Skull Rock. If we are printing the map, it is
important that we print it at full size. Otherwise, our answer when we
measure this distance will be different. It is also important that we
measure as accurately as possible although there will be a small margin for error in
most exams.

The distance on the map is equal to
7.2 centimetres. To get from one to 7.2, we multiply
by 7.2. This means that we need to multiply
400 by 7.2 to calculate the distance in metres. This is equal to 2880 metres. The straight line distance in
metres from Jack’s location to Skull Rock is 2880 metres.

If we didn’t have a calculator, we
could still work out this calculation, 400 multiplied by 7.2. We could do this by splitting 400
into four multiplied by 100. We could then firstly multiply 100
by 7.2. This is equal to 720 as multiplying
any number by two moves all the digits two places to the left. Four multiplied by 72 is equal to
288. Therefore, four multiplied by 720
is equal to 2880. This is the same answer as we got
on the calculator. The final part of the question says
the following.

d) Jack thinks that from Skull
Rock, he just has to walk 1600 metres to get to the Abandoned Fort. Why might he be incorrect?

The distance on the map between
Skull Rock and the Abandoned Fort is four centimetres. We know that the scale on the map
is one centimetre to 400 metres. This means that four centimetres on
the map would indeed be equal to 1600 metres. Multiplying one by four gives us
four. And multiplying 400 by four gives
us 1600. This initially suggests that Jack
is correct. He does have to walk 1600 metres to
get to the Abandoned Fort. However, we are looking for a
reason why he might be incorrect.

As mentioned in part c), we don’t
know whether he’s able to walk in a straight line from Skull Rock to the Abandoned
Fort. We also don’t know whether the land
or ground is flat. One reason why he might be
incorrect is that we don’t know the elevation of the island. The distance between the two places
would only be 1600 metres if it was completely flat. If the ground wasn’t completely
flat, the distance between the two points would be greater.

A different answer that would also
be correct is that we don’t know if he can walk in a straight line. This is the straight line distance
between Skull Rock and the Abandoned Fort. Once again, if he can’t walk in a
straight line, then Jack would walk a distance greater than 1600 metres.