Solving Word
Problems Using
Trigonometry
Ms. Baker
Taylor Road MS
March, 2013
New Vocabulary
Several new terms are used
in word problems, and you
need to know them!
Angle of Depression
Angle of Depression
In the diagram at the left, x
marks the angle of
depression of a boat at sea
from the top of a lighthouse.
You can think of the angle
of depression in relation to
the movement of your
eyes. You are standing at
the top of the lighthouse
and you are looking
straight ahead. You must
lower (depress) your eyes
to see the boat in the water.
Angle of Elevation
Angle of Elevation
The angle of elevation is always
measured from the ground up.
Think of it like an elevator that
only goes up. In the diagram at
the left, x marks the angle of
elevation of the top of the tree
as seen from a point on the
ground.
You can think of the angle of
elevation in relation to the
movement of your eyes. You
are looking straight ahead and
you must raise (elevate) your
eyes to see the top of the tree.
A little more information…
As seen in the diagram above of angle of
depression, the dark black horizontal line is parallel
to side CA of triangle ABC. This forms alternate
interior angles which are equal in measure (so, x
also equals the measure of BAC ).
Simply stated, this means that:
the angle of elevation = the angle of depression.
More about Angles of Depression
There are two possible ways to use
our angle of depression to obtain an
angle INSIDE the triangle.
1. Find the angle adjacent to our
angle which is inside the triangle.
This adjacent angle will always be
the complement of our angle. In
other words, the angles will add to
90º. In the diagram on the left, the
adjacent angle is 55º.
2. Utilize the fact that the angle of
depression = the angle of elevation
and simply place 35º in angle A.
(the easiest method) Just be sure
to place it in the proper position.
Subtended Angle
This is an angle formed by an
external point.
It’s easier to see, than describe…so
click on the link to see a great
example!
http://www.mathopenref.com/subtend.html
Your turn…
1. A ramp is to be placed from a
loading platform onto the back of a
truck. The truck can get no closer
than 3 feet to the platform. The truck
bed is 1.5 feet higher than the
loading platform. Find the angle of
elevation from the platform to the
truck bed.
Make a drawing!!
truck bed
1.5 feet
3 feet
loading platform
Now…Solve
1.5
tan  
3
1
tan (.5)  
  26.6
One more for good luck!
2. A jet is flying at an altitude of
30,000 feet. An air traffic
controller measures the angle of
elevation to the plane to be
16.5°. Find the horizontal
distance of the plane from the
airport.
Draw a picture! – It really
helps, I promise.
airplane
d
30000 feet
16.5°
d = Distance from airport
air traffic
controller
Solve!
30000
tan16.5 
d
d (tan16.5)  30000
30000
d
tan16.5
d  101278.3
So…The
airplane is
101278.3 feet
from the
airport.