Trigonometry

Trigonometry is a more advanced mathematics study of relationships of angles and lengths of each triangle. Basic formulae that have to be considered are:

Right angle trigonometry study

sin(x) = o/h
cos(x) = a/h
tan(x) = o/a

What are x, o, h and a etc.?

  1. x - the given angle.
  2. o - opposite side of the given angle.
  3. h - hypotenuse, the longer side that is not an opposite side of the given angle.
  4. a - adjacent side of the given angle (the third side that isn't opposite or hypotenuse).
  5. sin - Sinuse
  6. cos - Cosinuse
  7. tan - Tangent
Trigonometry diagram

Finding lengths

Finding lengths is a quite easy part. There's a triangle with 80 degree angle and it's adjacent side is 5cm. You need to find the opposite.
All you then need to do is to rearrange the trigonometry formula. You are going to need the tangent formula. currently, angle x:

tan(x) = o/a

The working:

tan(x) = o/a
o = a*tan(x)
o = 5*tan(80)
o = 28.3564091

Working on lengths

1) The angle of a triangle is 60 degrees. The opposite side of the triangle is 5cm length.
Find all the lengths.

Find out the hypotenuse:
sin(60)=5/h
h = 5 / sin(60)
h = 4.330127019
o = 5, h = 4.33, a = ?
Find out the adjacent:
tan(60) = 5/a
a = 5 / tan(60)
a = 8.660254038
o = 5, h = 4.33, a = 8.66

Finding angles

Finding angles is made easy too. You will need two lengths in order to a find a studied angle.
There are functions with -1 after sin, cos and tan names, which you need to use to find a required angle.

x = sin-1(o/h)
x = cos-1(a/h)
x = tan-1(o/a)

Working on angles

1) A triangle's opposite side of angle x is 5cm; the adjacent side is 8cm. Find x.

Formula used will be tangent formula:
x = tan-1(o/a)
x = tan-1(5/8)
x = tan-1(0.625)
x = 32.00538321 degrees
x = 32 degrees

See also

  1. Pythagoras' theorem
  2. Triangles