Students tend to have a lot of difficulties with word problems.
They usually aren't hard because of the math, but because of the words.
Students tend to have a difficult time translating the words of a word problem into a meaningful
picture or idea, which makes it extremely difficult to solve the problem.
So before we launch into a video about word problems, we will first talk through some
terminology that is used for these word problems.
The first two terms are angle of elevation and angle of depression.
These words refer to the angle above or below the horizontal.
Sometimes students get a little confused by this one because they draw the angle relative
to the slope of the ground instead of the horizontal.
For example, if you are on a downhill slope you will still need to sketch the horizontal
before drawing the angle of elevation.
Many problems involve motion most of the units should be familiar like meters per second
or miles per hour.
However, one unit you may see that you might not be familiar with are knots.
One knot is one nautical mile per hour.
A nautical mile is a minute of arc around the equator, where minutes refer to the degree-minute-second
notation for angles.
Fortunately, you should never need to convert out of nautical miles in order to complete
the problem, and so you won't need to know any conversions.
But just in case you're interested, a nautical mile is approximately 1.15 miles.
Another class of terminology relates to navigation and surveying problems.
Directions are often given in terms of bearings.
There are two different ways this is done, depending on the context.
One form of communicating bearings uses north as 0 degrees and increases as you turn clockwise.
This means that east is 90 degrees, south is 180 degrees, and west is 270 degrees.
So if someone's bearing is 230 degrees, they're facing in a direction between south and west.
These bearings are often used with compasses and hiking problems.
Another form of communicating bearings is to use either north or south as a reference
and then measure how far to the east or west from that reference they are facing.
For example, North 30 degrees East means that you start from north and turn 30 degrees to
the east.
A common mistake for these problems is to just plug in angles instead of thinking through
the entire direction.
For example, suppose we're traveling on a triangular path.
We start heading due east, then North 30 degrees West, and then finally South 60 degrees West
to return to the starting point.
Students often plug in numbers for the angles of the triangle without thinking about the
meaning of the words.
This leads to all sorts of problems.
The bearings given here are relative to the north-south line so you will need to draw
those in and measure the angles from there.
There are a couple different angle relationships that will help you to think through these
problems and to avoid errors.
If you have two parallel lines and a straight line that passes through them, the alternate
interior angles are congruent.
This arrangement happens often with navigation problems because the north-south line is often
used as a reference.
We also have that vertical angles and alternate exterior angles are congruent.
There will also be times when you will need to add or subtract angles from each other
to determine the angle you want.
For example, in this diagram the angle formed by the terminal sides is 15 degrees, and in
this diagram the total angle is 105 degrees.
In the next video we will work through a word problem that requires you to draw some diagrams
and think through some of these relationships.
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