Solving for Missing Sides Using Trig Ratios (Lesson 9.2)
Model situations using equations with trigonometric ratios.
Use trigonometric equations to solve for missing sides of a right triangle.
We’ll start today’s lesson with a video of Travis Pastrana breaking the world record for the longest car jump. After showing the video, students should work through questions #1-3 in their groups. In order to solve the equation in #3, you will need to show students how to use the trig functions in their calculators if they haven’t seen that before. (Make sure the calculators are set to degrees and not radians!!)
As you check in with groups, ask students to write their solutions on the board. By time you are ready to formalize with margin notes, all of the solutions should be written on the board already. (Huge time saver for you!)
In the last lesson we learned about trig functions. Which sides go with each ratio?
I notice your missing side is in the numerator, how could we get rid of the denominator so it’s all alone?
I notice your missing side is in the denominator, how could we get it out of the denominator?
The main goal today is to get students used to setting up equations with trig ratios to model a situation. When formalizing the experience, we want to point this out. We use the same process every time we approach one of these problems: draw a picture and “star” the angle we’re using, choose a trig function, write an equation, and solve. We’d recommend requiring students to show all of these steps on assessments as well. We make a question like this worth 2 points, a half point for each step.