GCSE Mathematics Higher Tier Topic Review : Trigonometry in 3 Dimensions
I can use Pythagoras in three dimensions
1. Find the distance from A to D.
D
2. Find the height of this pyramid.
12m
5m
C
A
8m
B
4m
8m
10m
I can find the angle between two lines
3. For the cuboid opposite, find the angles between these pairs of lines.
E
a) DC and HC
b) AB and BH
c) EB and BH
H
F
4m
D
A
4. The diagram shows two roads up a hill. Road A is
60m long and makes an angle of 24° with the
horizontal. Find the angle made by road B and the
horizontal.
G
C
B
7m
3m
A
B
60m
24°
100m
I can find the angle between a line and a plane
5. For the cuboid opposite, find the angles between...
a) GA and ABCD
b) GA and BCGF
c) FG and AEGC
H
G
E
F
4m
D
A
C
B
7m
3m
P
12m
6. Find the angle between PA and ABCD.
B
C
8m
D
A
10m
P
7. X is the midpoint of AB. Find the angle between PX and ABCD.
12m
C
X
B
8m
D
10m
A
GCSE Mathematics Higher Tier Topic Review : Trigonometry in 3 Dimensions
I can use Pythagoras in three dimensions
1. Find the distance from A to D.
D
2. Find the height of this pyramid.
12m
5m
C
A
8m
B
4m
8m
10m
I can find the angle between two lines
3. For the cuboid opposite, find the angles between these pairs of lines.
E
a) DC and HC
b) AB and BH
c) EB and BH
H
F
4m
D
A
4. The diagram shows two roads up a hill. Road A is
60m long and makes an angle of 24° with the
horizontal. Find the angle made by road B and the
horizontal.
G
C
B
7m
3m
A
B
60m
24°
100m
I can find the angle between a line and a plane
5. For the cuboid opposite, find the angles between...
a) GA and ABCD
b) GA and BCGF
c) FG and AEGC
H
G
E
F
4m
D
A
C
B
7m
3m
P
12m
6. Find the angle between PB and ABCD.
B
C
8m
D
A
10m
P
7. X is the midpoint of AB. Find the angle between PX and ABCD.
12m
C
X
B
8m
D
10m
A