## Wednesday, March 6, 2013

### Identifying the names of different sides of a right triangle

I have found that one reason my students have struggled with applying trigonometric ratios to mathematical scenarios is because they are unable to identify the differences between the "opposite" side, "adjacent" side, and the "hypotenuse". I decided to try to build up their vocabulary and boost their understanding of trigonometry at the same time.

First, I tackled the hypotenuse. My students were already familiar with the term, due to the Pythagorean Theorem. I reminded them that the hypotenuse is always the long side of a right triangle. I demonstrated that the long side is always the side opposite the right angle. Regardless of the way the triangle is "facing", the hypotenuse is always opposite the right angle.

I then told them that in trigonometry, they must think of themselves as looking at the triangle from the perspective of the angle they will be using in their trig function. I encouraged them to picture themselves standing at that angle and evaluating the triangle from there.

I asked my students what the word "adjacent" means. They seemed confused at first, so I asked them what it would mean if I said I was "adjacent" to my desk. One of my students suggested that I would be "next" to my desk. I encouraged this line of thought, and suggested that the "adjacent" side of the triangle is the side (other than the hypotenuse) that is touching the angle. The students were able to identify which side this is.

I then told them that the "opposite" side is the one that is opposite the angle - that is, that doesn't touch the angle at all. They were also able to identify this side.

After we discussed the names for the different sides of the triangles, it was much easier for the students to identify which trigonometric ratio they would use to find a missing side.