3 D Trigonometry Starter Can you find the

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3 D Trigonometry

3 D Trigonometry

Starter Can you find the value of x in this diagram to 2 dp?

Starter Can you find the value of x in this diagram to 2 dp? Be careful with rounding answers! 1) Start by finding the opposite side in the left triangle NOT TO SCALE Hyp 13 cm x 49. 82° 42° 8 cm Adj Opp 5. 93 4 cm 7. 20 24° Opp Hyp 12 cm Adj 2) Then subtract this from the hypotenuse of the lower triangle 5. 93 3) Then you can find the angle x by using the opposite and hypotenuse in the upper triangle

3 D Trigonometry • We have looked at using trigonometry in lots of situations

3 D Trigonometry • We have looked at using trigonometry in lots of situations • Today we will be focusing on using it in 3 D problems • The key to answering questions in 3 D is thinking about separate parts of them in 2 D • You will find that making quick sketches as you work will help you visualise what to do!

3 D Trigonometry ABCDEFGH is a cuboid, as shown. a) Calculate the length of

3 D Trigonometry ABCDEFGH is a cuboid, as shown. a) Calculate the length of BD 8. 06 cm (√ 65) b) Calculate the angle between BH and the base of the cuboid You can find the length of BD by just using the base H G 4 cm E 6 cm A F D 7 cm C 4 cm 7 cm Sub in values Add up B Square root (Remember that as an exact value, c = √ 65!)

3 D Trigonometry ABCDEFGH is a cuboid, as shown. a) Calculate the length of

3 D Trigonometry ABCDEFGH is a cuboid, as shown. a) Calculate the length of BD 8. 06 cm (√ 65) b) Calculate the angle between BH and the base of the cuboid To find the angle between BH and the base, draw on BH, and look to make a right angled triangle (inside the shape) H G Opp 6 E 6 cm F D √ 65 A θ C 7 cm 4 cm θ B √ 65 Adj Sub in values Calculate Use inverse Tan

Plenary The great pyramid of Giza is a square based pyramid of side length

Plenary The great pyramid of Giza is a square based pyramid of side length 230 m, and is 139 m 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? We need the length of the diagonal first 230 m Add up 230 m 325. 27 m 230 m Sub in values Square root

Plenary The great pyramid of Giza is a square based pyramid of side length

Plenary The great pyramid of Giza is a square based pyramid of side length 230 m, and is 139 m 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? Now we can draw the height on, and halve the length we just found… 139 m Opp 139 m 325. 27 m 162. 63 m 230 m 40. 5° θ 162. 63 m Adj Sub in values Calculate Use inverse Tan So you would be walking up at an angle of 40. 5°

Plenary The great pyramid of Giza is a square based pyramid of side length

Plenary The great pyramid of Giza is a square based pyramid of side length 230 m, and is 139 m 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? Now we can draw the height on, and halve the length we just found… So you would be walking up at an angle of 40. 5° 139 m 230 m 162. 63 m 230 m 40. 5° Sub in values Add up 162. 63 m Square root So you would have to walk a distance of 213. 9 m to the top!

Summary • We have looked at using Trigonometry in 3 D shapes • We

Summary • We have looked at using Trigonometry in 3 D shapes • We have seen how to model this using 2 D diagrams • We have seen that diagrams help a lot!!

Starter (printout) Can you find the value of x in this diagram to 2

Starter (printout) Can you find the value of x in this diagram to 2 dp? Be careful with rounding answers! NOT TO SCALE 13 cm x 42° 4 cm 8 cm 24° 12 cm

Plenary (printout) The great pyramid of Giza is a square based pyramid of side

Plenary (printout) The great pyramid of Giza is a square based pyramid of side length 230 m, and is 139 m 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?