4.8 Applications and Models

Remember the basic rules of right triangles. When one angle equals 90 degrees, the other two's sum is 90 degrees. Also, The sides of every right triangle can be found using the Pythagorean Theorem:

Side c is the hypotenuse and is always the longest side.

It is also worth noting that

Two terms to remember are angle of elevation and angle of depression. Both angles are measured from the horizontal.

Let's see some of these principles in action:

A plane is taking off from a runway 200 yards away from a 60 foot tall building. What is the minimum angle of elevation the plane must reach to not hit the building?

A great way to start these problems is to draw a picture and fill in the known quantities. Then, make your equation:

Our goal is to find x, so we use our previously mentioned equations to plug in the corresponding values. In this case it was tangent.

To get x by itself, take the inverse tangent of both sides:

The inverse tangent undoes the tangent of x. Now we use our calculator to solve:

Another point worth noting is that some story problems will give you bearings for directions that airplanes or boats are heading. They will look like this:

This means that the angle's initial side is pointing North and the angle's terminal side is 32 degrees East.