Lesson 10: Solving Right Triangles and Word Problems

Focus

Math 10C Module 1 Lesson 8

Module 1: Measurement and Its Applications

Lesson 10: Solving Right Triangles and Word Problems

** Always have your calculator in degree mode. Check by hitting the MODE button and looking at the third line. The word degree must be darkened**

Focus

This photo shows a metal bridge.

You may enjoy listening to music. The music may have been recorded digitally—a process that uses trigonometry. Perhaps the music is in MP3 format using data compression, which uses an understanding of the human ear’s ability to distinguish between sounds, and this format also requires trigonometry.

You may travel over a bridge today. That bridge was built using an understanding of forces acting at different angles. You will notice that bridges involve many triangles—trigonometry was used when designing the lengths and strengths of those triangles.

You will often see a surveyor at work in your community. Trigonometry helps the surveyor determine sides of a triangle that are difficult to access. An angle that cannot be reached may be measured from places that can be reached.

Earlier in the module, you saw an example of this principle when you read about building a tree house. The heights of trees and tall buildings can be determined by knowing the distance to the base of the tree or building. Similarly, distances across rivers or busy roads can be determined by using angle and length measurements from one side of the river or the road.

In the last two lessons you used the trigonometric ratios to find sides and angles in right triangles. In this lesson you will apply those skills to solve triangles ( finding all missing angles and sides) as well as solve real world problems.

Outcomes

At the end of this lesson, you will be able to

solve a right triangle ( find all missing sides and angles)
solve a problem that involves right triangles
solve a problem that involves one or more right triangles by applying the primary trigonometric ratios or the Pythagorean theorem
solve a problem that involves indirect measurement using the trigonometric ratios, the Pythagorean theorem, and measurement instruments such as a clinometer or a metre-stick

Lesson Questions

How do you approach problems whose solutions are based on trigonometry and its principles?
How is trigonometry used to determine heights and distances that cannot be directly measured?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Assess tab or by using the Quizzes link under the Activities block.

** Note – Share questions may have to be done on your own depending on your learning situation**