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.