1. Module 7

1.8. Page 3

Mathematics 10-3 Module 7 Lesson 2

Module 7: Trigonometry

 

Explore

 

In the Try This activity you will determine the height of an object, such as a building or a power pole, indirectly by using the tangent ratio.

 

But, first, review how the sides of a right triangle are identified by going to the applet titled “Right Triangle Side Names.”

 

Try This

 

In this Try This activity you will need your clinometer, a tape measure, and your calculator or square. If possible, work with a partner.

 

Step 1: Go outside and select an object that you would like to determine the height of. Examples include a power pole, a tall tree, or a building. The object should be on a flat, level stretch of ground because you will need to take measurements with your tape measure along the ground.

 

Step 2: From the base of the object, measure out a convenient distance. For a tree that might be 10 m tall, try not to be farther then 29 m from the object. Use your judgment.

 

Step 3: At the distance you selected, with the help of your partner, use your clinometer to determine the angle of elevation of the object’s top. You may wish to measure the angle several times and average your result to ensure accuracy. Then answer the questions that follow these steps.

 

Step 4: Also, measure the height your eye was above the ground when you used your clinometer.

 

TT 1. Draw a diagram similar to the following that describes your situation.

 

 

This illustration shows a vertical tree at the right. At the left is a point representing an eye. A horizontal line is drawn from this point to the tree, meeting the tree at a right angle. A line is drawn from the point to the top of the tree. The two lines and the included part of the tree form a right triangle.

 

TT 2. Use the tangent ratio to calculate the height of the object. Show all steps.

 

TT 3. Why did you need the height of your eye above the ground?

 

TT 4. How accurate is your calculated answer? What could you have done to improve the accuracy?

 

TT 5. Set up the identical situation in the “Exploring Trig Ratios” multimedia piece. Use this applet to check your calculation for TT 2. The following are hints to help set up your multimedia:

  • Use “Explore It” mode.

  • Choose “tan R.”

  • Determine if your unknown is the “Opposite” or “Adjacent” side.

  • Choose the “Reference Angle” (the angle you measured with the clinometer).