18) 3D Trigonometry
18) 3D Trigonometry
18) 3D Trigonometry
Starter
Can you find the value of x in this diagram to 2dp? Be
careful with rounding answers!
1) Start by finding the opposite 3) Then you can find the angle x by
side in the left triangle using the opposite and hypotenuse in
the upper triangle
NOT TO SCALE
Hyp
13cm
x
49.82
Opp
5.93
2) Then subtract this from the
4cm hypotenuse of the lower triangle
42
5.93
8cm
7.20
Adj Hyp
Opp
24
12cm
Adj
3D Trigonometry
We have looked at using trigonometry in lots of
situations
H G
4cm
E F 7cm
D C
6cm
Sub in values
4cm
Add up
A 7cm B
Square root
(Remember that as an exact value, c = 65!)
3D Trigonometry
ABCDEFGH is a cuboid, as shown.
a) Calculate the length of BD 8.06cm (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 F
D C
6cm 65
Adj
65 4cm
Sub in values
A 7cm B
Calculate
Use inverse Tan
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?
We need the length of the diagonal first
Sub in values
230m
Add up
Square root
230m
230m
325.27m
230m
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?
Now we can draw the height on, and halve the length
we just found
139m
Opp Sub in values
139m
Calculate
40.5 Use inverse Tan
230m
325.27m 162.63m
162.63m
Adj
230m 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 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?
Now we can draw the height on, and halve the length
we just found
139m
Sub in values
40.5 Add up
230m
162.63m
162.63m Square root
230m
So you would have to walk a distance
of 213.9m to the top!
Summary
We have looked at using Trigonometry
in 3D shapes
NOT TO SCALE
13cm
x
4cm
42
8cm
24
12cm
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?