Continued work on solving right triangles

Class time was spent today continuing to work on the Solving Right Triangle Using Trigonometric Ratios scenarios. While students made some progress at home, there was still a lot of uncertainty and confidence in what they were doing.

I gave the class some time to compare what they had done at home and finish finding solutions to the problems. As the class continued to work through the scenarios I could see that overall, they were gaining confidence in their work.

I asked students to put the numeric answers to problems 4-7 on the board. I then asked the class if they agreed with the answers or not. The only problem where there was a difference of opinion was for problem 4. I had the representation drawn on the board and everyone agreed that it was a correct representation. The differences came in which trigonometric ratio was most appropriate to use and in the algebraic process to solve the equation. When given the equation tan(35^o) = .7002 = 100 / x and asked to solve for x, there are still too many students who want to multiply both sides of the equation by 100. I asked students what happens if we multiply both sides of this equation by 100? On the left side, the result is 70.02. On the right, students started to recognize that the value is 100² / x or
10,000 / x. This caused some cognitive dissonance which got some students thinking about what value they would have to multiply by in order to move forward. They slowly began to realize what they needed to do was multiply by x and then divide by .7002.

I had students proceed on to the next set of problems. At this point, the class seemed comfortable with what they needed to do. As they got to problems 13-15, the only questions they were asking were clarification or to check that they were proceeding correctly. I left whatever they hadn't completed as homework. I also asked that they start work on the next six problem, which involve working with angle relationships of parallel lines. I reminded students about our work last semester so that they would remember that they have notes and resources to draw upon as the proceed ahead with these problems.