Trigonometry - Solving Triangles

Solving Triangles

This lesson is the next step in applying the three primary trigonometric ratios to solving triangles. Up until this point each lesson specifically focused on one of the three ratios and how to use that to solve for unknown angles and sides of a right-angle triangle. Now, we are applying all these skills to the same questions. 

When a question requires "solving a triangle" it's asking to solve for all three angles and all three side lengths. To do this requires selecting and choosing the appropriate trig ratio to use.

The video below outlines an example of steps to use to solve a triangle:

7.4 - Trigonometry - Solving Triangles 

Trigonometry - The Cosine Ratio

The Last Ratio

The Cosine Ratio is the last of our three primary trigonometric ratios. As a review go to the following google forms and test your knowledge:

Google Forms - SOH CAH TOA 

The cosine ratio is the ratio of the adjacent side to the hypotenuse of a reference angle. 

In this lesson we applied the cosine ratio to the same style of problems that we did the other two ratios. We practices solving for unknown angles and unknown side lengths. Through these three lessons we have learnt how to use the tangent, sine and cosine ratios to solve for unknown reference angles, unknown numerators in the ratio and unknown denominator in the ratio. The math processes used for each of the ratios is the same to solve for each unknown.

Primary Trigonmetric Ratio Acronym.
Chart Developed By Author.
Click for enlarged version.

The key difference with each ratio is the side length that corresponds to the numerator and denominator of the ratio. In the lesson we discussed the use of the acronym SOH CAH TOA to help remember the orientation of each ratio. The chart I build and we used is pictured to the left. Using SOH CAH TOA to work backwards and rebuild the ratio equations is a great way to make sure the ratios are properly orientated. I told the students that the first thing I do when I write a quiz or test using the primary trig. ratios is write the acronym at the top of my page. 

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Comparing The Sine Ratio and The Cosine Ratio
Chart Developed by Author.
Click for enlarged version.

Another comparison we looked at in this lesson was the relationship between sine and cosine. As a class we built a chart that looked at how the ratio for sine and cosine was affected with increasing angle values. For sine we found that as the angle value increased the ratio increased from 0 to 1. For cosine we found that as the angle value increased the ratio decreased from 1 to 0. When comparing the two ratios we found that at each increment in the chart on the left the value of the ratio corresponded to the invert of the other's value. 

Click the following link to access this lesson's video:

7.4 - Trigonometry - The Cosine Ratio

Trigonometry - The Sine Ratio

This video looks at how we can use the sine ratio to solve for unknown sides of a right angle triangle and unknown angles of a right angle triangle.

The sine ratio of a reference angle is equivalent to the ratio of the opposite side to the hypotenuse side of a right angle triangle.

If you were comfortable with the math from the previous video/lesson this math should also make sense. The way we apply the sine ratio is identical to the tangent ratio with only key difference. While the tangent ratio looks at the ratio of opposite side to the adjacent side the side ratio looks at the ratio of the opposite side to they hypotenuse side.

Created using Google Draw by Author.
You can click this image to enlarge it.

Using the sine ratio we can solve a few different trigonometric problems. The sine ratio has three variables (a reference angle, the opposite side length and the hypotenuse's side length), of which we need two to be given to be able to solve for the third. This relates to the problems we can solve using the tangent ratio.










Follow the link below for this lesson's video:

7.4 - Trigonometry - The Sine Ratio

**NOTE: The sine ratio can NEVER be a value greater than 1. Since the demominator in the ratio is the hypotenuse, which is the longest side of a right angle triangle the numerator will always be smaller than the denominator. A ratio that has the numerator smaller than the denominator the is always equivalent to a value less than

Trigonometry - The Tangent Ratio

This lesson was the looks at the first of three primary trigonometric ratios.

There are a few key take away ideas from this video/lesson:

1. The importance of checking to make sure you have a right angle triangle is at the three sides are labeled correctly with Hypotenuse, Opposite and Adjacent.
2. Using the tangent ratio to solve for an unknown angle.
3. Using the tangent ratio to solve for and unknown opposite side (numerator).
4. Using the tangent ratio to solve for an unknown adjacent side (denominator). 

A few tips to keep in mind when solving these problems:

• Make sure you calculator is set to Degrees and not Radians.
• Make sure you are consistently getting the correct answer on your calculator. Some times it can be difficult to properly enter the math into your calculator, also some calculators require it to be entered differently. 

The link to this video is below: 

7.3 - Trigonometry - The Tangent Ratio

Trigonometry - Solving Similar Triangles

7.2 - Solving Similar Triangles

This is my second attempt at making a video to complement a lesson I facilitated in a grade 10 academic math course. I felt the last video was a little difficult to follow as I filled in all the information as I went using my trackpad on my computer - resulting in long pauses in my explanations while I struggled to write close to legibly. This time I used the filled in note from class and verbally walked through the steps and explanations of each of the problems. I mentioned that I would be making two videos for this lesson one similar to the last and one as I have just described. In hindsight I think this video turned out pretty well; if feedback from students tells me otherwise I will make a supporting video similar to the last published video. 

This lesson looks at the properties of similar triangles and uses this understanding to solve for various combinations of sides and angles of similar triangles. 

Follow the link below for access to the video:

Youtube + Whiteboard Video - 7.2 Solving Similar Triangles

Trigonometry - Review of Essential Skills

Introduction to Trigonometry

This was my first attempt at recording a smart board lesson. I don't currently have a mouse on my laptop so the writing portion of it was a little slow and a little messy (okay maybe a lot messy.)

Feel free to use this recording to listen to my explanations of MPM 2D introduction to trigonometry - review of essential skills. Pausing and replaying certain parts could work as a great strategy if you struggle with any concepts.

Full disclosure: I make a few mistakes when referencing the various angle relationship theorems. I think I correct myself for the most part though.

Click the link below to go to the video.

7.0 - Review of Essential Skills

About This Blog

I will be using this blog as a compliment to my teaching practicum. The goal for this blog is to provide students with two things:

• Video recap of lessons taught. 
• Additional problems. 

By using this resource students will be able to review any of the lessons in the unit. This can be used as a daily tool to ensure the knowledge is really sinking in or as a review tool before quizzes or the test.