We finished our Rational Expressions and Equations test this week, so we’ve started our new unit. Trigonometry. So I’m gonna post everything I remember from Trigonometry in grade 10.

In a right triangle, the side closest to theta that isn’t the hypotenuse is the adjacent side. The side farthest is the opposite side, and the hypotenuse remains the same, like always.

Remember SOH CAH TOA

SOH is

 

CAH is

 

TOA is

 

To find an angle when you have the lengths of two sides, you can use the inverse of sine, cosine, or tangent. Say you had this triangle. You want to find the angle of B. Well, that makes the 5cm side the opposite side, and the 7cm side the hypotenuse. We don’t know how long the adjacent side is, so we can’t use that. So which ratio can we use? We can use Sine, because

So to find the angle of B, we take the inverse sine of 5/7.

 

And of course, with some algebra skills, you can also also find the length of one side if you have the length of another side and an angle.

Don’t forget, you can also use the Pythagorean theorem to find the length of another side if you need to.