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Math 10C Module 1 Lesson 8

Module 1: Measurement and Its Applications

 

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Glossary Terms

 

 Add these terms to your glossary:

  • angle of depression
  • angle of elevation
  • clinometer
  • congruent triangles
  • similar triangles

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Solving Right Triangles

Read

Find out how to solve a triangle when you are given different measures of a triangle. Read the textbook that you are using for this course.

Pay attention to the numbers that are used in each calculation. Every time a new measure is calculated, one more number can be used to determine the next unknown measure.

What reasons are there for using the original given measures? What reasons are there for using calculated measures?

 

Foundations and Pre-calculus Mathematics 10 (Pearson)

 

Read “Example 1: Solving a Right Triangle Given Two Sides” on pages 106 and 107 to see two methods for solving a right triangle given two sides.

 

Read “Example 2: Solving a Right Triangle Given One Side and One Acute Angle” on page 108 to see how to solve a right triangle given the measure of one length and one acute angle.


Watch and Listen

Watch the following Khan Academy Video to get a better understanding of what it means to Solve a Right Triangle.


Try This 1

Use what you have learned in this lesson to solve some triangles. Remember to use a calculated value to solve for another value only if you are sure of the correctness of the calculated value. If the calculated value is incorrect, then the subsequent values will also be incorrect.

Complete the following in your course folder ( binder).

Foundations and Pre-calculus Mathematics 10 (Pearson), question 6 on page 111.

Use the link below to check your answers to Try This 1.

Possible TT1 (Try This 1) Solutions

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Solving Word Problems

This illustration shows a diagram of a man looking at a tree. A right triangle is superimposed on the diagram where the hypotenuse is the distance between the man’s eyes and the top of the tree.

man, house, tree: Image Club ArtRoom/Getty Images

Sometimes you will see either the expression angle of elevation or angle of depression when you are solving a word problem involving angles.

 

The angle of elevation is the angle from the horizontal to the line of sight as shown in the diagram.

 

The angle of elevation is useful to know in problems where the observer is looking upwards at something.

 

This illustration shows a man looking down at an object from a point of higher elevation. The angle of depression is shown as the angle between the horizontal and the line of sight.

man: Image Club ArtRoom/Getty Images

           The angle of depression, on the other hand, refers to those instances when the observer is looking downwards at something. Like the angle of elevation, the angle of depression is the angle between the horizontal and the line of sight. The difference is that the line of sight, in this case, is directed downwards. **IMPORTANT** Do NOT put the angle of depression between the vertical and then line of sight. This is a COMMON error.
  Try This 2

What is the relationship between the angle of elevation and the angle of depression? Try the following exercise to see if you can discover what the relationship is.

 Read the following scenario and complete the following in your course folder ( binder)

Romeo is standing in Juliet’s yard. Juliet, meanwhile, is standing on her balcony three stories above the ground. Each one is looking at the other person.

Step 1. Sketch a simple diagram showing this scenario. Place a copy of your sketch in your course folder.
Step 2. In your sketch, use a ruler to draw Romeo’s line of sight to Juliet.
Step 3. Show the angle of elevation from the horizontal to his line of sight. Add it to your sketch.
Step 4. In your sketch, show the angle of depression from the horizontal to Juliet’s line of sight. (Hint: Juliet’s line of sight is the same as Romeo’s.)
Step 5. Use a protractor to measure the angle of elevation and the angle of depression. What do you notice?

Use the link below to check your answers to Try This 2.

Possible TT2 (Try This 2) Solutions