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== 4.856.5440180B

cmbb

B

b

A

a

39.104.85sin40sin

7.6

sinsin

=

=

=

cmbCB 39.10and6.54,4.85 ===

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2. In the triangleABC,AB = 5cm, BC =10cm,

CA = 8cm, If X is the mid-point of themedian

AA, find the length ofBX.

=+=

+=

==

4.52

cos)10)(5(21058

cos))((2

5''

222

222

B

B

BBCABBCABAC

cmCABASolution:

A B

C

10cm

5cm

8cmA

X

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cmAAXA

cmAA

AA

BBAABBAABAA

2075.2'

2

1'

415.4'

4927.19

4.52cos)5)(5(255'

cos)')((2''

222

222

==

==

+=

+=

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( )

cmBX

BX

AXABAXABABX

A

49.4

1268.20

8.63cos)2075.2)(5(22075.25

'cos)')('(2''

8.634.521802

1'

222

222

==

+=

+=

==

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3.

D

BA

P

C

bb

a

a

For rectangleABCD shown

in the figure above,AB =BC = b.The foot of theperpendicular fromA to BDis P. Calculate the lengthsofAP and CP.

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Solution

:

2222

22

2222

sin

sin

ba

abAPa

AP

ba

b

a

AP

AB

APABD

ba

b

BD

+==+

==+

==

+=+=

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D

P

C

a

CDPDPCDDPCDCP

ba

aCDP

ABDCDP

+=

+=

=

cos))((2

costhen

222

22

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( )( )

( ) ( )

( )

21

22

2244

22

2244

22

224224

22

224222

2222

22

22

22

222

2

2

2

cos))((2

++

=

++

=+

++=

+ ++=

+

+

++=

+=

ba

babaCP

ba

baba

ba

babbaa

bababbaa

ba

a

ba

ba

ba

ba

CDPDPCDDPCDCP

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4. In the triangle PQR, PQ = a, QR = a + d, RP

=a+2d, and , where a and

dare

positive constants. Show that

> 120PQR.

3

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( )

( ) ( )

PQRQRPQQRPQPR

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( )

( ) ( )( )