SOLVING TRIG EQUATIONS
Remember: SOH CAH TOA
Triangle ABC
TOA
In this triangle we need to find the value of the x angle since we know the length of the side opposite the reference angle and the side adjacent to the angle we will use tangent to find the value of the angle, since we are finding the value of the angle as opposed to the sides we will have to inverse tangent. The value of 
This first equation is rather simple, all we have to do is punch the numbers into our calculator.
When we are representing it with variables the equation looks like this:
The full equation would be:
Triangle xyz
SOH
In this triangle we are trying to find the value of n which is the hypotenuse, because we know side opposite of the reference angle and because we are also finding the hypotenuse we will use sine to find it.
In variable form the equation is: 
With numbers the equation is:
Because it’s harder to calculate with a variable as the denominator we reciprocate.
To get the value of n:
This equation in its simplest form would be:
Triangle DEF
CAH
In this triangle we are trying to find the value of x which is the adjacent, we will be using cosine because we have the value of the hypotenuse and we are trying to find the adjacent.
The equation looks like this:
To remove the denominator we have to multiply both sides by the denominator like so:
Simplified our final answer is:
I am certain that my answers make sense because of two things: 1. The angles match up with their opposite side, large angles have long sides and small angles have short sides respectively. 2. The hypotenuse is the longest side, the highest value an angle can be in a right triangle is 90 degrees which is opposite the hypotenuse, so when we use the Pythagorean Theorem to find the value of all the other sides the hypotenuse will always be the longest side.