To perform calculations we are going to use the triangle above.
The three main relationships are:

Tan(x) = o/a
Sin(x) = o/h
Cos(x) = a/h

so if h = 5 and x = 30
a = Cos(30)h = 4.330

We can also use a inverse of the functions
ie) x = tan^-1(o/a)
x = sin^-1(o/h)
x = cos^-1(a/h)

so if o = 5 and a = 10
x = tan^-1(5/10) = 26.565

Using this information we can work out any side or angle in a right angled triangle as long as we have to other pieces of information (like a side and a angle or 2 sides). This is used a lot in resolving forces in physics and allows us to derive some other more complex equations.

Also see

• Trigonometry Identities (11)
• Sec, Cosec, Cot (0)
• Tan = sin/cos (6)
• CAST Diagarams for finding values of sin, cos and tan between 0 and 360 or 2 pi (0)
• Tan Graph – y=tan(x) (0)
• Compound Angles – sin(A+B) = cosAsinB+sinAcosB (6)