Trigonometry

What is trigonometry? It only works for right angle triangles It is useful in building and surveying to work out the height of buildings It is used by aeroplanes and space shuttles landing to make sure they do not crash

How does it work? First you need to be able to label the parts of a triangle The easiest is the longest side, the hypotenuse Where is it? Hypotenuse (it is always opposite the right angle)

Labelling the sides You need to identify which angle (not the right angle) we know There are two other sides The opposite is the side opposite the angle, where is it? The adjacent is the other side, beside it. Where is it? Hypotenuse Opposite Adjacent

SOHCAHTOA These are the equations you need to use to work out the angle They are; S=O/H Sin = Opposite/Hypotenuse C= A/H Cosine = Adjacent/ Hypotenuse T=O/A Tan = Opposite/ Adjacent

Working Out One Side If you want to find an unknown side you first have to work out which part of SOHCAHTOA you are going to use E.g. We know the hypotenuse and we need to find the opposite side (x) Which equation do we use? Sin = O/H Sin is a button on the calculator Sin72 = X/10 0.95 = x/10 9.5m = x (this is smaller than the hypotenuse) 10m x 72°

Try these: 15cm w x 53° 72° 8cm 49° z 12cm y 65° 12cm

Answers X = 14.3cm Y = 5.1cm W = 10.6cm Z = 9.1cm

Finding An Angle To find an angle you divide the two sides you know and press shift sin/cos/tan E.g. We want to find out what angle a is? Which equation do we use? Cos = A/H Cos a = 5/10 Cos a = 0.5 A = 60° 10cm a° 5cm

Try these: F ° 7cm 25cm 15cm 8cm G ° 5cm 9cm 10cm 6cm H ° I °

Answers F = 57.8° G = 73.7° H = 36.9° I = 29.1°