A builder's level is focused on a
graduated stick called a Philadelphia rod with markings
divided into feet and decimal parts of a foot.
So in our diagram, this is the builder's level
and we actually have three red Philadelphia rods.
One, two, and three.
The first sighting is on a measurement above
a fixed reference point called the benchmark.
So our benchmark is this point here with a known elevation
of 105.50 feet,
or 105 and 50 hundredths feet.
Let's take a look at our questions.
We first want to determine the height of the instrument
which we can think of as
the elevation of the builder's level.
Next, we want to find the elevation at point A,
the elevation at point B,
and then the finding the difference in elevation
between point A and point B.
So let's start by determining the height of the instrument,
which again we can think of
as the elevation of this builder's level
or the builder's level line of sight.
To do this we'll be using the benchmark
as well as this first reading.
If the benchmark elevation at 105.50 feet,
that means the elevation of the builder's level
to this point here,
would also be 105.50 feet.
So if I take the benchmark and we add
the first reading, which would be the distance from
the line of sight to the benchmark,
which should also be the same as
the distance from here to here,
this will give us the height of the instrument.
So we'd have 105.50 feet
plus 4.75 feet.
Remember when adding decimals,
we want to lap the corresponding place values
and the decimal point.
So bring the decimal point down
and then we'll add the corresponding place values
from right to left.
So zero plus five is five.
Five plus seven is 12,
so I put a two in the tenths' place value
and carry a one to the ones' place value,
and the ones' we have one plus five plus four, that's 10,
so I have a zero in the ones' place value.
We carry a one to the tens' place value.
We have a one in the tens' and a one in the hundreds'.
So the height of the instrument is 100.25 feet
or 110 and 25 hundredths feet.
So again we can think of the line of sight
of having an elevation of
110.25 feet.
This is important because this will help us find
the remaining elevations at point A and point B.
So to find the elevation at point A, this point here,
notice how the elevation to this line of sight, again,
is 110.25 feet,
and the elevation that we want is below this
and the length from the line of sight to point A
is the reading of 6.23 feet,
or six and 23 hundredths feet.
So to find the elevation of point A, we'll have to take
the height of the instrument and subtract
the reading of 6.23 feet.
Again, lining up the place values and the decimal point.
Bring the decimal point down, subtract from right to left.
So five minus three is two, two minus two is zero.
Here we have a zero in the ones' place value
so we can make an exchange here with the tens' place value
if we take one from here this would be zero
leaving us with 10 ones, 10 minus six is four,
and then we have a zero and one.
So the elevation at point A is 104.02 feet,
or 104 and two hundredths feet.
Now we'll find the elevation at point B.
And again, point B is here,
so to find the elevation at this point,
we'll take the height of the instrument
and subtract the reading here of 3.92 feet,
which should be this distance here.
That would give us the elevation at point B.
So you have 110.25 feet
minus 3.92 feet.
Bring down the decimal point,
and we'll subtract from right to left.
Five minus two is three.
Here we'll have to borrow or exchange
all the way over from the tens' place value,
so we would change the one to a zero.
This would be ten ones but we're going to exchange
a ones' for tenths', so this would be nine
and this would be 12 in the tenths' place value.
So we have 12 minus nine is three.
Nine minus three is six
and then we have a zero in the tens' place value
and a one in the hundredths'.
So the elevation at point B
is 106.33 feet,
or 106 and 33 hundredths feet.
Notice how point B is higher than point A
and that's good because notice how the elevation
is greater at point B than point A.
Now let's take a look at our last question.
We want to determine the difference in elevation
between point A and point B.
Since the elevation is higher at point B,
we'll take the elevation at point B
and subtract the elevation at point A.
So three minus two is one, three minus zero is three,
six minus four is two, zero minus zero is zero,
and one minus one is zero.
So I can say the elevation at B
is two and 31 hundredths feet
or 2.31 feet higher
than the elevation at A.
I hope you found this helpful.