Upload
stuart5051
View
230
Download
0
Embed Size (px)
Citation preview
8/14/2019 Trigo Extra
1/62
8/14/2019 Trigo Extra
2/62
8/14/2019 Trigo Extra
3/62
== 4.856.5440180B
cmbb
B
b
A
a
39.104.85sin40sin
7.6
sinsin
=
=
=
cmbCB 39.10and6.54,4.85 ===
8/14/2019 Trigo Extra
4/62
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
8/14/2019 Trigo Extra
5/62
cmAAXA
cmAA
AA
BBAABBAABAA
2075.2'
2
1'
415.4'
4927.19
4.52cos)5)(5(255'
cos)')((2''
222
222
==
==
+=
+=
8/14/2019 Trigo Extra
6/62
( )
cmBX
BX
AXABAXABABX
A
49.4
1268.20
8.63cos)2075.2)(5(22075.25
'cos)')('(2''
8.634.521802
1'
222
222
==
+=
+=
==
8/14/2019 Trigo Extra
7/62
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.
8/14/2019 Trigo Extra
8/62
Solution
:
2222
22
2222
sin
sin
ba
abAPa
AP
ba
b
a
AP
AB
APABD
ba
b
BD
ADABD
baABADBD
+==+
==+
==
+=+=
8/14/2019 Trigo Extra
9/62
8/14/2019 Trigo Extra
10/62
D
P
C
a
CDPDPCDDPCDCP
ba
aCDP
ABDCDP
+=
+=
=
cos))((2
costhen
222
22
8/14/2019 Trigo Extra
11/62
( )( )
( ) ( )
( )
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
8/14/2019 Trigo Extra
12/62
4. In the triangle PQR, PQ = a, QR = a + d, RP
=a+2d, and , where a and
dare
positive constants. Show that
> 120PQR.
3
2ada 1200
8/14/2019 Trigo Extra
13/62
( )
( ) ( )
dada
dad
dada
dada
adadadaadada
daadaada
PQRQRPQQRPQPR
8/14/2019 Trigo Extra
14/62
( )
( ) ( )( )
ad
ad
adadadaadada
daadaada
QRPQQRPQPR