3D Trigonometry Starter Can you find the value of x in this diagram to 2dp? Be careful with rounding answers! 12cm 24 8cm x 42 4cm 13cm Opp Adj Hyp Adj 7.20 5.93 5.93 Opp Hyp 1) Start by finding the opposite side in the left triangle 2)
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Presentation Transcript
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3D Trigonometry<br>
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Starter Can you find the value of x in this diagram to 2dp? Be careful with rounding answers! 12cm 24° 8cm x 42° 4cm 13cm Opp Adj Hyp Adj 7.20 5.93 5.93 Opp Hyp 1) Start by finding the opposite side in the left triangle 2) Then subtract this from the hypotenuse of the lower triangle 3) Then you can find the angle x by using the opposite and hypotenuse in the upper triangle 49.82° NOT TO SCALE<br>
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3D Trigonometry We have looked at using trigonometry in lots of situations
Today we will be focusing on using it in 3D problems
The key to answering questions in 3D is thinking about separate parts of them in 2D
You will find that making quick sketches as you work will help you visualise what to do!<br>
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3D Trigonometry ABCDEFGH is a cuboid, as shown.
Calculate the length of BD
Calculate the angle between BH and the base of the cuboid H G F E D C B A You can find the length of BD by just using the base 7cm 4cm 7cm 4cm 6cm Sub in values Add up Square root (Remember that as an exact value, c = √65!) 8.06cm (√65)<br>
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3D Trigonometry ABCDEFGH is a cuboid, as shown.
Calculate the length of BD
Calculate the angle between BH and the base of the cuboid H G F E D C B A 7cm 4cm 6cm 8.06cm (√65) θ √65 To find the angle between BH and the base, draw on BH, and look to make a right angled triangle (inside the shape) √65 6 θ Opp Adj Sub in values Calculate Use inverse Tan<br>
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Plenary The great pyramid of Giza is a square based pyramid of side length 230m, and is 139m high. If you were to stand in one corner and walk up the pyramid to the top, what angle would you be walking up at and how far would you have to walk? 230m 230m We need the length of the diagonal first 230m 230m Sub in values Add up Square root 325.27m<br>
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Plenary The great pyramid of Giza is a square based pyramid of side length 230m, and is 139m high. If you were to stand in one corner and walk up the pyramid to the top, what angle would you be walking up at and how far would you have to walk? 230m 230m Now we can draw the height on, and halve the length we just found… 325.27m 162.63m 162.63m 139m 139m θ Opp Adj Sub in values Calculate Use inverse Tan 40.5° So you would be walking up at an angle of 40.5°<br>
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Plenary The great pyramid of Giza is a square based pyramid of side length 230m, and is 139m high. If you were to stand in one corner and walk up the pyramid to the top, what angle would you be walking up at and how far would you have to walk? 230m 230m Now we can draw the height on, and halve the length we just found… 162.63m 162.63m 139m 139m 40.5° So you would be walking up at an angle of 40.5° Sub in values Add up Square root So you would have to walk a distance of 213.9m to the top!<br>
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Summary We have looked at using Trigonometry in 3D shapes
We have seen how to model this using 2D diagrams
We have seen that diagrams help a lot!!<br>
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Starter (printout) Can you find the value of x in this diagram to 2dp? Be careful with rounding answers! 12cm 24° 8cm x 42° 4cm 13cm NOT TO SCALE<br>
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Plenary (printout) The great pyramid of Giza is a square based pyramid of side length 230m, and is 139m high. If you were to stand in one corner and walk up the pyramid to the top, what angle would you be walking up at and how far would you have to walk?<br>
