Cambridge International Mathematics

Trigonometry (Chapter 15) 335

2 For each of the following figures, name the angle between the given line segment and the base plane:

aiDE ii CE

iii AG iv BX

biPY ii QW

iii QX iv YQ

ciAQ ii AY

3 For each of the following figures, find the angle between the given line segments and the base plane:

aiDE

ii DF

iii DX

iv AX

biPU

ii PV

iii SX

ciKO

ii JX

iii KY

diXD

ii XY

THE ANGLE BETWEEN TWO PLANES

Suppose two planes meet in a line.

We choose a point P on the line, and draw AP in one plane so it

is perpendicular to the line. We then draw BP in the other plane

so that BP is perpendicular to the line and so that AbPB 690 o.

The angle μ=AbPB is defined as the angle between the two

planes.

Example 15 Self Tutor

A square-based pyramid has base lengths 6 cm and height 8 cm.

Find the angle between a triangular face and the base.

The base:

) ¢ABT is the required angle.

Now tanÁ=^83 ,so Á= tan¡^1 (^83 )¼ 69 : 4 o:

The angle is about 69 : 4 o:

H G

X

E F

D C

AB

X Z

S

P Q

R

Y

W

A

Q

P

S

R

X

Y

H G

X

E F

D C

AB

10 cm

10 cm

10 cm

WV

U

T

S R

P Q

10 cm

4cm

6cm

X

4m

4m

3m

NOX

JK

YM L

12 cm

10 cm

15 cm

A B

Y

D C

M

X

A

B

line

P

q

T B

A

8cm

f

3cm

P

Q

R

S

A

B

T f

3cm

P Q

S R

T

B

AB is perpendicular to QR and

TB is perpendicular to QR

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Y:\HAESE\IGCSE01\IG01_15\335IGCSE01_15.CDR Tuesday, 7 October 2008 2:26:45 PM PETER