Inverse Trig Functions for Missing Angles (Lesson 9.3)

Learning Targets
  • Use similar triangles to find missing angle measures. 
  • Use inverse trigonometric functions to solve for missing angle measures. 
Activity: Missing Angles

Experience First

Students should be able to work through this entire activity in their groups with minimal support from the teacher. Begin by having students brainstorm everything they know about similar triangles. Have groups share out what they remember with the class. From there, groups can work through the rest of the front page. As always, have students write their answers on the board. If groups get stuck, try these guiding questions to keep them moving.

Guiding Questions

  • What does it mean for triangles to be similar? 

  • In the last lesson, we talked about using trig functions to find missing sides. Are there any trig functions that will help you here?

  • What do you notice about all of the triangles in question #2? What about the triangle in question #3?

Formalize Later

At the end of the first page, explain how we now know that any right triangle that has              has an angle                   What what if                    ? Then what? I tell my students that there is a table that has every single cosine value and the corresponding angle but it’s huge! But guess what? Your calculator stored it all for you! Then show them how to use  in their calculators.


After you go through the QuickNotes, give students plenty of time to work through the Check Your Understanding (CYU)problems. The goal in the experience today was for students to understand what an inverse trig function tells us and why it works. In the CYU, they’ll get to practice applying them, which can be a tough leap. You may want to help students draw the picture for the Flight 1549 problem (#3) and help them convert the miles to feet.

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