Sine, cosine and tangent ratios are numbers you get by labelling the sides hypotenuse, opposite and adjacent on a right triangle and dividing them by each other to get one of these ratios.

O = Opposite
H = Hypotenuse
A = Adjacent

Labelling a right triangle is very simple, first look for your hypotenuse, it should be across from the square indicating the right angle in the triangle almost as if it’s pointing to it, to label the other two sides look for a reference angle typically indicated by an x or just an angle, the side furthest from this reference angle is called the opposite and the side closer or next to the angle is called the adjacent. After labelling these we can get to dividing the length of the sides by each other.

A sine ratio goes , a cosine ratio goes , and a tangent ratio goes . In a case where O = 3 and A = 4 and you’re trying to solve for a reference angle you first get your ratio which would be tangent in this case, divide the numerator by the denominator to get rid of the fraction and have a decimal instead, currently we have a problem that looks like this:

tan x = 0.75 now using a calculator, inputting 0.75 get us our answer of approximately 36.7° as our reference angle.

In a case where you have a missing side to solve you use the given side and reference angle to solve for them, for example if you have an A = 4 and AH = 30°, only solving for H would go like this;

cos 30 = is our first step where we just write down everything we are given, the next step goes = H as you need to isolate the variable and reciprocate what you moved, if the variable is on the bottom of the ratio the number will be getting divided by the sin, cos, or tan and if the variable is at the top of the ratio you instead multiply the number by the sin, cos, or tan when you reciprocate. From here we input 4 ÷ (cos 30) into a calculator which gets us approximately 4.6 as our H here.

Those are ways you can solve for a missing angle or a missing side length, thanks for reading.