Trigonometry What is trigonometry It only works for

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? x 10 m Sin = O/H Sin is a button on the calculator Sin 72 = X/10 72° 0. 95 = x/10 9. 5 m = x (this is smaller than the hypotenuse)

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

Answers • X = 14. 3 cm • Y = 5. 1 cm • W = 10. 6 cm • Z = 9. 1 cm

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? 10 cm a° 5 cm Which equation do we use? Cos = A/H Cos a = 5/10 Cos a = 0. 5 A = 60°

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

Answers • F = 57. 8° • G = 73. 7° • H = 36. 9° • I = 29. 1°