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Trigonometry Objectives of this slideshow •Identify opposite, hypotenuse and adjacent sides • Define SOCAHTOA •Apply SOCAHTOA depending on which rule we need •Use all of the above to help find missing angles in a right angled triangle •Calculate missing sides of a right angled triangle given another angle and length of one side. Hypotenuse opposite adjacent Label the opposite, adjacent and B hypotenuse C A Top tips always find: •Hypotenuse first as this is the easiest (always opposite the right angle) •Opposite second as it is always opposite the angle we are interested in •Finally the adjacent (which means next to) this one is the only one left and is next to the angle but is not the hypotenuse A = adjacent B = opposite C = hypotenuse Does theopposite, angle Label the adjacent, and we are looking at hypotenuse here. make a difference toIf you thehave names any of B the questions write them sides? C on your whiteboard A A = adjacent B = opposite C = hypotenuse YES IT DOES!!!! A = opposite B = adjacent C = hypotenuse You need to remember this Sine = opposite hypotenuse Cosine = adjacent hypotenuse Tangent = opposite adjacent You should be able to tell what the size of this angle is using your knowledge of triangles. Step We are label going theto sides proveH,this O and A (this order) The1: two sides are using trigonometry. The equal length so it Step 2: work out which reason picked an angle must beI have an isosceles trigonometric function we that we already know is so triangle. It can’t need to use basedbeonanthe info that we can be sure we are equilateral we are given.asInone thisofcase we getting theiscorrect answer thegiven angles rightA are the Oa and which using trigonometry which we angle. relates to tangent because are unfamiliar with. Once we Tangent = O/A have familiar with it 180° –become 90° = 90° we can start looking at more difficult that we can 6cm 90° ÷ 2 =examples 45° only solve using trigonometry. The be 45° Stepangle 3: themust tangent of this angle = 6/6 =1 to find the actual angle we do tan¯¹ (1) = 45° 6cm Have a go at this question to see if you can find the yellow angle? Click to the next screen for a little help 5cm Step 1: label the sides H, O and A 13cm Step 2: which function do you use? SOHCAHTOA Step 3: use the sine rule because sine = opp/hyp and these are the two we know. Opp/hyp = 5/13 Sine¯¹ = Tip if the answer you get seems like a wrong answer check through the steps that you have labelled the sides correctly, used the correct function and if not you probably didn’t press the inverse function. You probably pressed Sine and not Sine¯¹. Cosine¯¹(13/9) = ____ why??? Don’t shout out your answer!!! Because cosine is adjacent/hypotenuse and the hypotenuse is always the biggest side. In this case the adjacent side was bigger than the hypotenuse therefore impossible to do. 3cm Draw these triangles in your book (not to scale) and then work out the missing angle Sine (O/H) sine¯¹(3/4) = 48.6° (1dp) Sine (O/H) tangent (O/A) tangent¯¹(6/5) = 50.2° (1dp) sine¯¹(4/7) = 34.8° (1dp) Find all the missing angles 3cm Draw these triangles in your book (not to scale) and then work out the missing angle Sine (O/H) sine¯¹(3/4) = 48.6° (1dp) Sine (O/H) tangent (O/A) tangent¯¹(6/5) = 50.2° (1dp) sine¯¹(4/7) = 34.8° (1dp) Find the length of the side labelled x Step one what rule do we need to use? Sine because we know the hypotenuse and we want to know the opposite This time we can say that We can multiply both sides By 15 to get sine(45 °) = 15 x sine(45 °) = 10.61cm(2dp) = X 15cm X X Find the length of the side labelled x Step one what rule do we need to use? Cosine because we need to know the hypotenuse and we do know the adjacent This time we can say that We can multiply both sides By X to get Then we can divide both sides by Cosine (45 °) Cosine(45 °) = 8cm X X Cosine(45 °) = 8cm X = 8cm ÷ Cosine(45 °) X = 11.31cm (2dp) Draw these triangles in your book (not to scale) and then work out the missing angle x 60° 45° 52° 36° Show the angle is 45° on any right angled isosceles triangle using trigonometry