Day 5: Students will define tangent and it relationship to slope. Tangent is the trig function you use to find either the opposite or adjacent side of a triangle when you are given either the opposite or adjacent side and an angle within the triangle. So, for example, you would use tangent if you knew what the length of the opposite side and an angle in the triangle were but needed to find the length of the adjacent side. Tangent relates to slope because to find slope you need to know rise and the run of a triangle, and to use tangent you need to know either the opposite or adjacent side of a triangle and you are trying to find either the opposite or adjacent side of a triangle; the rise and the run of a triangle are the adjacent and opposite sides.

Quiz:

1. What two sides of a triangle are associated with tangent?
2. If the opposite side of a triangle is 4 and the adjacent side of the triangle is 1, what is the slope of the triangle?
3. If you you know that the opposite side of a triangle is 2 and the angle of the triangle is 50 degrees, what is the length of the adjacent side?

Answer Key:

1.

The two sides are the adjacent side and the opposite side.

2.

The slope is 4/1.

3.

The length of the adjacent side is 1.67 units.