You have explored various properties of the tangent function. Next, you will look at how some problems can be solved using the tangent function.

Try This 5

Open Airplane Exploration. The applet shows a plane flying in a straight line at a height of 6000 m over an observer on the ground. (Each unit represents 1000 m in the applet.)

1. At the observer, an angle is formed between a vertical line and the plane. Determine a relationship between this angle and the horizontal distance, d.
2. Copy and complete the following table of values.
   
   

   Angle	50°	45°	25°	10°	0°	−10°	−25°	−45°	−50°
   Horizontal Distance (d) from Observer

3. Extend the table of values from question 2 to include values from –90° to 90°.
4. Use your table of values to sketch the graph of this relationship.

Save your answers in your course folder.

Share 3

With a partner or group, discuss the following questions based on the relationship you determined in Try This 5.

1. Where are the asymptotes on your graph? What do the asymptotes represent in the scenario?
2. What happens when the angle is equal to 0°? What does an angle of 0° represent in the scenario?

If required, save a record of your discussion in your course folder.