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Mathematics Form 4 : Chapter 11 Lines and Planes in 3-Dimensi

11.1 Angle Between A Line And A Plane

1. PM!""#$%1%14

Diagram shows a cuboid with a horizontal base TUVW. The angle

between the line PW and the base TUVW is

2. PM !""4$%!%4

Diagram shows a cuboid. Calculate the angle between the

line AH and the plane ABCD.

3. PM!""&%P!%4'3 mar(s)

Diagram shows a right prism. The base P!"# is a horizontal

rectangle. "ight angled triangle !"U is the uni$orm cross%section

o$ the prism. V is the midpoint o$ P#. &denti$' and calculate the

angle between the line UV and the plane "#TU.

4. PM!""*%P!%11'3 mar(s)

Diagram shows a cuboid( is the midpoint o$ the side)H and A(*+ cm.

,a- ame the angle between the line A( and the plane

AD)/.

,b- Calculate the angle between the line A( and the plane

AD)/.

5. PM 1++&

The diagram shows a cuboid.

Calculate the angle between the line )H and the plane H012.

6. PM !""4%1%14

ame the angle between the line !V and the plane !U".

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7. PM !"""

The diagram shows a right prism with isosceles triangle UWT as

its uni$orm cross section. ( and are midpoints o$ P! and UT

respecti3el'. 4i3en that PU*5 cm6 UT*7 cm and UW*WT*+ cm.

Calculate the angle between the line W( and the plane P!TU.

8. Diagram 8 shows a right prism with an isosceles

triangle base6 #TU. The isosceles triangle #TU is the

uni$orm cross%section o$ the prism. #T * #U and W is

the midpoint o$ TU. Calculate the angle between the

line PW and the base #TU.

9. PM !""1

The diagram shows a cuboid. 9 is the midpoint o$ TW.

Calculate the angle between the line !9 and the plane TUVW.

10. PM 1+++

The diagram shows a cuboid. ( is the midpoint o$ !".

Calculate the angle between the line U( and the plane

P!"#.

11. PM 1++3

The diagram shows a cuboid. ( and are midpoint o$ #" and

WV respecti3el'. Calculate the angle between the line T( and the

plane TUVW.

12. PM 1++&$

The diagram shows a cuboid. ( is the midpoint o$ TW.Calculate the angle between the line (! and the plane

P!"#.

W

13

cm

10

cm

12

cm

P Q

R

S T

U

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13. PM 1++#$

The diagram shows a cuboid.

ame the angle between the line #/ and the plane )/4H.

14. PM 1++,$

The diagram shows a cuboid. ( and are midpoints o$

!" and VW. 4i3en P(*: cm and WV*8 cm.

ame the angle between the line P and the plane P!"#.

15. PM !""#$%!%4

Diagram shows a right prism. The base H012 is a horizontal

rectangle. The right angled triangle H0 is the uni$orm cross

section o$ the prism. &denti$' and calculate the angle between the

line 1 and the plane H2(.

16. PM 1++*$

The diagram shows a right prism with a horizontal

rectangular base 12(. "2(# is a trapezium. U and T

are midpoint o$ 1 and 2( respecti3el'.Calculate the angle between the line !( and the plane

12(.

17. PM 1++*

The diagram shows a triangular prism with a horizontal

rectangular base P;"#. T#P is a right%angled triangle.

Calculate the angle between the line !T and the plane P!"#.

18. #P(5:

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19. PM 1++,

He diagram shows a triangular prism. ( and are midpoint o$ P#

and !" respecti3el'. 4i3en that PT*+ cm and !"*8 cm.

ame the angle between the line PU and the plane P!"#.

20. PM 1++#

The diagram shows a p'ramid with a horizontal

rectangular base P!"#. U and V are midpoint o$ !" and

P# respecti3el'. TV*7 cm is 3ertical and !"*TU*: cm.

Calculate the angle between the line T! and the plane

P!"#.

21. PM !"",%1%14

What is the angle between the line V/ and the base )/4H>

22. PM !"",$%1%14

Diagram shows a right p'ramid P!"# with its s?uare

base P!"#. The angle between the line ! and the baseP!"# is

23. PM 1++4

The diagram shows a p'ramid with a horizontal triangular base

PT#. "ectangle !"#T is a 3ertical plane.

ame the angle between the line P" and the plane !"#T.

24. PM !""4%!%3

Diagram shows a p'ramid V012(. The base 012( is a

horizontal rectangle. ! is the midpoint o$ 0(. The ape@ V

is 7 cm 3erticall' abo3e the point !. Calculate the angle

between the line 1V and the base 012(.

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25. #P(5:5U

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30. Diagram shows a right prism with a horizontal

rectangular basePQRS. VUQR is a trapezium. MandN

are the midpoints o$PSand QRrespecti3el'. Calculate the

angle between the line TR and the basePQRS.

31. Diagram : shows a cuboid with a rectangular base

PQRS.M andNare midpoints o$ TUandPQ

respecti3el'.

Calculate the angle between the line #( and the plane

TUVW

T

U

W

V

P

Q

R

SM

N

7 cm

8 cm

5 cm

+ cm

P

5= cm

cm

+ cm

T M U

Q

R

N

W

S

V