Intro To Trigonometry

Question

I am learning about basic Trig functions (SohCahToa) and am having trouble determining when a side is the adjacent and when the side is opposite, This seems like a basic concept, and yet there is something I am missing. I do know that the opposite side is opposite to an angle given, and the adjacent side is next to a given angle. But what if a Right Angle is all that is given? Opposite that angle is a hypotenuse, and both the other sides are both next to the given Right Angle. Can anybody make sense of my confusion?

Thank You,

Brian

Answer 1

This explanation would be a little clearer if video answer was available, but video answers are not available right now.

So, here goes.

An angle consists of two rays with a common endpoint.. In a right triangle there are two acute angles. Let's say one of those angles is angle A. Angle A consists of a ray that lies along the hypotenuse (endpoint is point A) and another ray that lies along a leg of the triangle. The ray that has endpoint A and lies along the leg is adjacent to angle A. It is the other leg that is opposite angle A.

Let's say we have right triangle DEF with angle E the right angle. If you want to determine the leg that is adjacent to angle F (for example) , picture tracing two rays starting at point F. One of those rays will lie along the hypotenuse (segment FD). The other ray will lie along leg FE. Leg FE is adjacent to angle F. That means leg DE is opposite angle F. Notice how the opposite leg does NOT contain the letter F (or point F).

To summarize:the adjacent side contains the endpoint of the ray that is part of the angle in question. The opposite side does not. Be sure to sketch right triangle DEF as you read the above..

Answer 2

In triangles, it requires at least 3 things to be given to define the triangle. So, if you are only given the right angle, there isn't enough information. For instance, here are two triangles, both with the same "right angle", both with the same length of hypotenuse, but they are different triangles:

Usually when we are talking about SOHCAHTOA, we are refering to an angle other than the right angle (but having a right angle is mandatory).

The opposite side is the side you point to if you come straight out of the angle with a ray that is an angle bisector like this:

The adjacent side is actually connected to the angle (but it's the connected segment that is not the hypotenuse) like this: