There’s three different sides to a triangle:
- The hypotenuse is the longest side
- The opposite is the side opposite to the angle being used in the question
- The adjacent is the side next to the angle being used in the questionWhenever you have a trigonometry question you need to find the two sides involved and pick the formula that is correct.
Note: These only work for right angled triangles!A useful way of remembering these equations is SOH CAH TOA.
When you get a question involving trig, label the sides of the triangle correctly then write out SOH CAH TOA and see which equation you are dealing with.
You can then write the correct one as a formula triangle:Then cover up what you want to find with your finger and the formula you are left with is what you use.
So if you were using the CAH triangle, and wanted to find the hypotenuse you would cover up the H with your finger. You then know to find this you need to divide the adjacent by cos x.
Angle Of Elevation And Depression
Trig comes up a lot in this type of question.
The angle of depression is just the angle upwards from the horizon and the angle of depression is the angle downwards from the horizon.These are always equal!
In such a question a right angled triangle is formed.
Example: A person 100 meters from the base of a tree observes that the angle between the ground and the top of the tree is 18 degrees. Estimate the height h of the tree to the nearest tenth of a meter.So here we have the adjacent side and we need to find the opposite. Therefore we are dealing with TOA and using our formula triangle we can see:
Opposite = tan 18 x 100 = 32.49196…
So the answer is 32.5m