Reflection: Continuous Assessment Area of Triangles - Section 2: Finding Area of Triangles


As I was looking at student work I started to notice that many of the students were only using the Law of Sines and Law of Cosines.  The students were not seeing that the altitude was making a right triangle with the base.  Instead of doing the sin A= opp side/hypotenuse they would use Law of Sines with the 90 degree angle.  

I would ask the students to look at the triangle.  Isn't that a right triangle? When is the Law of Sines defined? (of course students can use the Law of Sines with right triangles and it can be used to prove the right triangle properties but our definition was that the Law of Sines and the Law of Cosines is for oblique triangles.)

Once I brought the type of triangle to the students attention, I found out they had 2 issues with the right triangle ratios. The first was that they did not remember the ratios. The other issue was that some students were still struggling with what is meant by the opposite and adjacent sides.  I even had students try to use the ratios by saying cos 90 = one leg/hypotenuse. To clear this up I ask the students what the opposite side was and how could this side be the opposite side and the hypotenuse at the same time.  I also reviewed that the ratios are for acute angles and 90 is not acute.

My other thought about only using Law of Sines and Law of Cosines is that these were the newest formulas learned so the students assumed that this would be what I was practicing.  I am hoping the students will learn that when we do a problem solving activity any concepts can be used not just the most recent.

  Continuous Assessment: Not seeing right triangles
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Area of Triangles

Unit 6: Solving Problems Involving Triangles
Lesson 10 of 13

Objective: SWBAT find the area of triangles when given sides and angles of possible triangles.

Big Idea: Why does (1/2)*a*b*sin(C) give the area of a triangle?

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