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
which is the angle