Cambridge International Mathematics

Trigonometry (Chapter 15) 333

5 All edges of a square-based pyramid are 12 m in length.

a Find the angle between a slant edge and a base diagonal.

b Show that this angle is the same for any square-based pyramid with all edge lengths equal.

SHADOW LINES (PROJECTIONS)

Consider a wire frame in the shape of a cube as shown in the diagram

alongside. Imagine a light source shining down directly on this cube from

above.

The shadow cast by wire AG would be EG. This is called theprojection

of AG onto the base plane EFGH.

Similarly, the projection of BG onto the base plane is FG.

Example 12 Self Tutor

Find the shadow or projection of the following onto the base

plane if a light is shone from directly above the figure:

a UP b WP

c VP d XP.

a The projection of UP onto the base plane is UT.

b The projection of WP onto the base plane is WT.

c The projection of VP onto the base plane is VT.

d The projection of XP onto the base plane is XT.

THE ANGLE BETWEEN A LINE AND A PLANE

The angle between a line and a plane is the angle between the line and its projection on the plane.

Example 13 Self Tutor

Name the angle between the following line segments

and the base plane EFGH:

a AH b AG.

H G

F

E

D C

AB

W

V

T U

S R

P Q

X

W

V

T U

S R

P Q

X

W

V

T U

S R

P Q

X

H

G

E F

D C

A

B

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_15\333IGCSE01_15.CDR Thursday, 2 October 2008 9:41:32 AM PETER