These four definitions are needed to understand right angle trigonometry:
- The hypotenuse is the side opposite the right angle, also the biggest side.
- The opposite side is the side opposite to the angle you are looking at.
- The adjacent side is the side that connects with the right angle, from the angle you are working at.
- A right angle, is one equivalent to 90 degrees.
An easy way to remember the functions are SOH CAH TOA or S = O/H, C = A/H, T = O/A
Here are the equations for right triangle trig:
- Sine (sin) = Opposite/Hypotenuse.
- Cosine (cos) = Adjacent/Hypotenuse.
- Tangent (tan) = Opposite/Adjacent.
And the three remaining functions are reciprocals of the first three.
- Cosecant (csc) = Hypotenuse/Opposite
- Secant (sec) = Hypotenuse/Adjacent
- Cotangent (cot) = Adjacent/Opposite
For the following examples, use the right triangle, ABC, at the right. Notice that B is a right angle, and b is the hypotenuse. Also note that A is the angle being worked with, therefore a is the opposite side, and c is the adjacent side.
Example 1: If side a equals 12, and side c equals 24, find angle A. (notice that this is a sine function, because the opposite and hypotenuse sides are given)
| Step 1: | Set up your equation | a/(sin 30) = 11/(sin 40) |
|---|---|---|
| Step 2: | Cross multiply | a(sin 40) = 11(sin 30) |
| Step 3: | Finish solving | a( ) = 11( ) |
| a = |
Example 2: If angle A equals 39 degrees, and side b equals 23, find side c. (The cosine function will be needed in this problem, because the adjacent and hypotenuse sides are involved.
| Step 1: | set up equation | cos(39) = c/23 |
|---|---|---|
| Step 2: | Solve | .777 = c/23 |
| Step 3: | Multiply to isolate c | 23 x .777 = c |
| 17.87 = c |
Here are a few other websites you might find useful:
The math page, right angle trig.
Bdaugherty, right angle trig.
