Finding a Side in a Right Angled Triangle
You can find a Side if you know another Side and Angle
We can find an unknown side in a rightangled triangle if we know:
 one length, and
 one angle (apart from the right angle, that is).
ExampleFind the height of the plane. 
We know one length (1000) and one angle (60°), so we should be able to solve it, but how?
The answer is to use Sine, Cosine or Tangent!
But which one to use? We have a special phrase "SOHCAHTOA" to help us, and we use it like this:
Step 1: find the names of the two sides you are working on: the side you already know, and the side you are trying to find:

In our example:
 the one we know is the Hypotenuse
 the one we are trying to find is Adjacent to the angle (check for yourself that "h" is adjacent to the angle 60°)
Step 2: now use the first letters of those two sides (Adjacent and Hypotenuse) and the phrase "SOHCAHTOA" to find which one of Sine, Cosine or Tangent to use:
SOH... 
Sine: sin(θ) = Opposite / Hypotenuse 
...CAH... 
Cosine: cos(θ) = Adjacent / Hypotenuse 
...TOA 
Tangent: tan(θ) = Opposite / Adjacent 
In our example that is Adjacent and Hypotenuse, and that gives us “sohCAHtoa”, which tells us we need to use Cosine.
Step 3: Put our values into the Cosine equation:
cos 60° = Adjacent / Hypotenuse = h / 1000
Step 4: Now solve that equation!
But how do we calculate "cos 60°" ... ?
You use your calculator! type in 60 and then use the "cos" key. That's easy! 
cos 60° = 0.5 (by my calculator)
So now we can put "0.5" instead of "cos 60°":
0.5 = h / 1000
Now all that is left is to rearrange it a little bit:
Start with:  0.5 = h / 1000  
Swap sides:  h / 1000 = 0.5  
Multiply both sides by 1000:  h = 0.5 x 1000 = 500  
The height of the plane = 500 meters
Step By Step
These are the four steps to follow:
 Step 1 Decide which two sides we are using  one we are trying to find and one we already know – out of Opposite, Adjacent and Hypotenuse.
 Step 2 Use SOHCAHTOA to decide which one of Sine, Cosine or Tangent to use in this question.
 Step 3 Write down the fraction Opposite/Hypotenuse, Adjacent/Hypotenuse or Opposite/Adjacent, whichever is appropriate (one of the values will be the unknown length)
 Step 4 Solve using your calculator and your skills with Algebra
Examples
Let’s look at a few more examples:
Example: Find the length of the side a: 
 Step 1 The two sides we are using are Opposite (a) and Adjacent (7).
 Step 2 SOHCAHTOA tells us we must use Tangent.
 Step 3 Write down the fraction for tan 53° = Opposite/Adjacent = a/7
 Step 4 Solve:
Start with:  tan 53° = a/7  
Swap:  a/7 = tan 53°  
Calculate tan 53°:  a/7 = 1.32704…  
Multiply both sides by 7:  a = 1.32704… × 7 = 9.29 (to 2 decimal places)  
Side "a" = 9.29
Example
The angle the cable makes with the seabed is 39° and the cable's length is 30 meters. Find the depth "d" that the anchor ring lies beneath the hole in the ship’s side. 
 Step 1 The two sides we are using are Opposite (d) and Hypotenuse (30).
 Step 2 SOHCAHTOA tells us we must use Sine.
 Step 3 Write down the fraction for sin 39° = opposite/hypotenuse = d/30
 Step 4 Solve:
Start with:  sin 39° = d/30  
Swap:  d/30 = sin 39°  
Calculate sin 39°:  d/30 = 0.6293…  
Multiply both sides by 30:  d = 0.6293… x 30 = 18.88 to 2 decimal places.  
The depth the anchor ring lies beneath the hole is 18.88 m
Example
There is a mast that is 70 meters high. A wire goes to the top of the mast at an angle of 68°. How long is the wire? 
 Step 1 The two sides we are using are Opposite (70) and Hypotenuse (x).
 Step 2 SOHCAHTOA tells us we must use Sine.
 Step 3 Write down the fraction for sin 68° = 70/w
 Step 4 Solve:
The unknown length is on the bottom (the denominator) of the fraction!
So we need to follow a slightly different approach when solving :
Start with:  sin 68° = 70/w  
Multiply both sides by w:  w × (sin 68°) = 70  
Divide both sides by "sin 68°":  w = 70 / (sin 68°)  
Calculate:  w = 70 / 0.9271... = 75.5 m (to 1 place)  
The length of the wire = 75.5 m