In order to solve problems involving angles of
elevation and depression, it is necessary to
A typical problem of angles of
elevation and depression involves organizing information regarding distances and angles within a right triangle. In some cases, you will be asked to determine the measurement of an angle; in others, the problem might be to find an unknown distance.
Suppose a tree 50 feet in
height casts a shadow of
length 60 feet. What is the
angle of elevation from the end of the shadow to the top of the tree with respect to the ground?
First we should make a diagram to organize our information. Look for these diagrams to involve a right triangle. In this case, the tree makes a
angle 90º with the ground. A diagram of this
right triangle is shown below.
In the diagram, known distances are labeled. These are the 50 and 60 foot legs of the
right triangle corresponding to the
height of the tree and the
length of the shadow.
The
variable q is chosen to represent the unknown measurement, the object of the question.
To relate the known distances and the variable, an
equation is written. In this case the
equation involves the lengths of the sides which are opposite and adjacent to the
angle q. Using the
ratio of opposite to adjacent sides, we have
.
We use
inverse tangent of
or
which is the
angle of elevation.