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A B C 35 o 52 o 54 o 38 o A B C M N ( AB = = ( MN A B C D I
A B C h yp othén use côté adjacen t à ¸ côté opp osé à ¸ ¸ A B C h yp othén use côté opp osé à ˛ côté adjacen t à ˛ ˛ A B C D E F
ChingQuizz
:
6
exercises
a v ailable
for
Quizz
assessmen t
:
1.
Reminders
on
angles
E.6436
Determine
the
mea- sure
of
the
angle
∠
BC A
:
E.6437
Consider
a
triangle
ABC
such
that
:
∠
BAC
=
54
o
;
∠
ACB
=
38
o
The
p oin ts
M
and
N
belong
to
the
segmen ts
[
AC
]
and
[
BC
]
respectiv ely
and
are
suc h
that
(
AB
)
==
(
MN
)
.
Determine
the
measure
of
the
angle
∠
MN C
.
E.9015
Consider
the
rectangle
ABC D
such
that
∠
DAC
=65
o
.
The
p oin t
I
of
the
diagonal
[
AC
]
is
placed
suc h
that
the
triangle
ABI
is
righ t-angled
at
I
:
1
Determine
the
measure
of
the
angle
∠
DC A
.
2
Determine
the
measures
of
all
the
angles
of
triangles
ADC
,
AIB
and
BI C
.
2.
Intro duction
E.9017
Definition:
in
a
righ t
triangle :
the
side
opp osite
the
righ t
angle
is
called
the
hy- p othèn use
relative
to
an
angle
carried
b y
the
h yp oten use,
the
other
side
of
the
angle
is
called
the
side
adjacen t
to
the
an- gle
and
the
other
side
is
called
the
side
opp osite
the
angle
.
Consider
the
t w o
righ t-angled
triangles
ABC
and
DE F
re-sp ectiv ely
righ t-angled
at
B
and
F
shown
b elo w
:
1
a
Name
the
triangle
mortgage
ABC
.
b
Name
the
side
adjacen t
to
the
angle
∠
BAC
.
2
Name
the
side
opp osite
the
angle
∠
FD E
https:/ /c hingmath.fr
chapExoCorrec/6436 sacados/6436 A B C 35 o 52 o chapExoCorrec/6437 sacados/6437 54 o 38 o A B C M N ( AB = = ( MN chapExoCorrec/9015 sacados/9015 A B C D I chapExoCorrec/9017 sacados/9017
A B C h yp othén use côté adjacen t à ¸ côté opp osé à ¸ ¸ A B C h yp othén use côté opp osé à ˛ côté adjacen t à ˛ ˛ A B C D E F
A 1 B 1 C 1 25 o A 2 B 2 C 2 25 o A 3 B 3 C 3 25 o A 4 B 4 C 4 25 o A B C h yp othén use cos ¸ AC AB ¸ A B C h yp othén use cos ˛ BC AB ˛ A B C H
E.4917
W e
consider
the
four
triangles
sho wn
b elo w
are
righ t-angled
and
ha v e
an
angle
of
25
o
.
1
Using
the
measuremen ts
in
the
figure
ab o v e,
complete
the
table
b elo w,
rounding
the
lengths
to
the
nearest
mil- limeter :
Triangle
1
2
3
4
Hypotén use
Side
adjacen t
à
the
corner
of
25
o
2
Using
the
calculator,
giv e
the
v alues
of
the
quotien ts
re- quested
rounded
to
the
nearest
h undredth
:
Triangle
1
2
3
4
Longueur
from
the
side
adjacen t
to
the
corner
of
25
o
Longueur
de
l’h yp otén use
E.9029
Definition-proposition :
In
a
righ t-angled
triangle,
for
an
acute
angle
¸
of
this
triangle,
w e
define
the
cosine
of
the
angle
α
by
the
v alue
of
the
quotien t
:
Longueur
of
the
side
adjacen t
to
the
angle
¸
Longueur
of
the
h yp oh ten use
The
v alue
of
this
quotien t
do es
not
dep end
on
the
dimen- sions
of
the
righ t-angled
triangle,
but
only
on
the
measure
¸
of
the
angle :
it
is
noted
cos(
α
)
Example
1 :
Consider
the
triangle
ABC
shown
b elo w
où
the
p oin t
H
is
the
fo ot
of
the
heigh t
arising
from
the
p oin t
C
.
1
In
the
triangle
ABC
,
giv e
as
a
function
of
the
lengths
of
the
segmen ts,
an
expression
of
the
trigonometric
ratios
:
a
cos
∠
BAC
b
cos
∠
ABC
2
a
In
the
triangle
ACH
,
giv e
an
expression
for
cos
∠
CAH
b
In
triangle
BC H
,
giv e
an
expression
of
cos
∠
CB H
https:/ /c hingmath.fr
chapExoCorrec/4917 sacados/4917 A 1 B 1 C 1 25 o A 2 B 2 C 2 25 o A 3 B 3 C 3 25 o A 4 B 4 C 4 25 o chapExoCorrec/9029 sacados/9029 A B C h yp othén use cos ¸ AC AB ¸ A B C h yp othén use cos ˛ BC AB ˛ A B C H
A B C 4 ; 9 cm 6 ; 7 cm D E F 14 k m 43 k m 43 o 71 o 4 ; 9 6 ; 7 0 ; 731 14 43 0 ; 326 6 k m 3 , 2 k m 6 , 8 k m A B C 2 8 o 8 m m 3 , 9 m m 8 , 9 m m D E F 2 6 o
A B C M N C 1 10 o C 2 C 3 C 4 A B A B C 5 cm 25 o G I H 3 cm 35 o
E.6439
Example:
(angles
have
b e en
r ounde d
to
the
ne ar est
de gr e e)
Consider
the
t w o
triangles
ABC
and
DE F
belo w
:
Giv e
the
follo wing
v alues
rounded
to
the
nearest
h undredth
:
a
cos
28
b
cos
64
Hint :
cosine
v alues
for
all
angles
from
1
o
to
89
o
are
all
kno wn
and
a v ailable
on
a
table
or
using
the
calculator :
E.3579
Consider
the
triangle
AMN
right- angled
M
;
the
p oin ts
B
and
C
belong
to
the
segmen ts
[
BC
]
and
[
MN
]
respectiv ely ;
the
line
(
BC
)
is
p erp endicular
to
the
line
(
AM
)
:
1
Using
a
graduated
ruler,
giv e
an
appro ximate
v alue
for
the
side
measures
of
the
t w o
triangles
ABC
and
AMN
.
2
Using
a
calculator,
compare
the
appro ximate
v alues
of
the
follo wing
t w o
quotien ts
:
BC
AC
;
MN
AM
3
a
Justify
that
the
lines
(
BC
)
and
(
MN
)
are
parallel.
b
Justify
the
equalit y
of
the
follo wing
t w o
quotien ts
:
BC
MN
=
AC
AN
c
Deriv e
the
follo wing
equalit y :
BC
AC
=
MN
AN
d
Compare
this
equalit y
with
y our
results
from
question
1
.
W as
there
an
error
in
y our
calculations?
Where
d
the
error
come
from?
4
Using
measuremen ts
and
appro ximate
v alues,
compare
the
pairs
of
quotien ts
b elo w
:
a
AB
AC
;
AM
AN
b
BC
AC
;
MN
AM
E.1154
Let
ABC
4
be
a
righ t-angled
trian- gle
at
B
.
The
angle
C
4
AB
measures
40
o
,
it
is
divided
in to
four
angles
of
the
same
measure
using
the
p oin ts
C
1
,
C
2
,
C
3
belonging
to
the
segmen t
BC
4
1
Using
y our
graduated
ruler,
w e’ll
giv e
the
measuremen ts
of
the
lengths
rounded
to
the
nearest
millimetre.
The
quotien ts
in
the
last
column
will
b e
rounded
to
the
near- est
h undredth
:
i
BAC
i
AC
i
AB
AC
i
1
2
3
4
2
Complete
the
follo wing
table
using
the
cos
key
on
y our
calculator.
The
v alues
are
rounded
to
the
nearest
thou- sandth
:
¸
10
o
20
o
30
o
40
o
cos(
¸
)
3.
Use
of
the
c osine :
se ar ch
for
the
adjac ent
side
E.4919
Consider
the
four
triangles
sho wn
b elo w
:
https:/ /c hingmath.fr
chapExoCorrec/6439 sacados/6439 A B C 4 ; 9 cm 6 ; 7 cm D E F 14 k m 43 k m 43 o 71 o 4 ; 9 6 ; 7 0 ; 731 14 43 0 ; 326 6 k m 3 , 2 k m 6 , 8 k m A B C 2 8 o 8 m m 3 , 9 m m 8 , 9 m m D E F 2 6 o chapExoCorrec/3579 sacados/3579 A B C M N chapExoCorrec/1154 sacados/1154 C 1 10 o C 2 C 3 C 4 A B chapExoCorrec/4919 sacados/4919 A B C 5 cm 25 o G I H 3 cm 35 o
E D F 3 ; 5 cm 75 o J L K 6 ; 5 cm 20 o A B C 6 cm 33 o G I H 3 cm 65 o J L K 4 ; 5 cm 40 o E D F 1 ; 5 cm 48 o
10 o A B C 4 ; 5 cm 20 o J K L 1 ; 5 cm 75 o
Determine
the
lengths
of
the
follo wing
segmen ts.
Round
y our
answ ers
to
the
nearest
millimeter :
a
[
AC
]
b
[
GH
]
Hints :
Below
is
part
of
the
trigonometric
table
for
cosine.
¸
o
cos
¸
o
¸
o
cos
¸
o
¸
o
cos
¸
¸
o
cos
¸
o
¸
o
cos
¸
o
0
o
1
20
o
0
;
94
40
o
0
;
766
60
o
0
;
5
80
o
0
;
174
5
o
0
;
996
25
o
0
;
906
45
o
0
;
707
65
o
0
;
423
85
o
0
;
087
10
o
0
;
985
30
o
0
;
866
50
o
0
;
643
70
o
0
;
342
90
o
0
15
o
0
;
966
35
o
0
;
819
55
o
0
;
574
75
o
0
;
259
E.9025
Consider
the
four
triangles
sho wn
b elo w
:
Determine
the
lengths
of
the
follo wing
segmen ts.
Round
y our
answ ers
to
the
nearest
millimeter :
a
[
EF
]
b
[
KJ
]
Hints :
Below
is
part
of
the
trigonometric
table
for
cosine.
¸
o
cos
¸
o
¸
o
cos
¸
o
¸
o
cos
¸
¸
o
cos
¸
o
¸
o
cos
¸
o
0
o
1
20
o
0
;
94
40
o
0
;
766
60
o
0
;
5
80
o
0
;
174
5
o
0
;
996
25
o
0
;
906
45
o
0
;
707
65
o
0
;
423
85
o
0
;
087
10
o
0
;
985
30
o
0
;
866
50
o
0
;
643
70
o
0
;
342
90
o
0
15
o
0
;
966
35
o
0
;
819
55
o
0
;
574
75
o
0
;
259
E.6440
W e
consider
the
four
triangles
rep- resen ted
b elo w
:
Determine
the
measure
of
the
lengths
of
the
follo wing
seg- men ts
rounded
to
the
nearest
millimeter :
a
[
AB
]
b
[
GI
]
4.
Use
of
the
c osine :
se ar ch
for
the
hyp othenuse
E.9027
W e
consider
the
four
triangles
rep- resen ted
b elo w
:
Determine
the
measure
of
the
lengths
of
the
follo wing
seg- men ts
rounded
to
the
nearest
millimeter :
a
[
EF
]
b
[
KJ
]
E.9020
A t
an
acrobatic
park,
managemen t
w an ts
to
install
a
new
zip
line.
The
cable
will
b e
installed
at
a
heigh t
of
8
m
in
heigh t
and
the
slop e
of
the
cable
m ust
b e
10
o
.
Determine
the
length
of
cable,
rounded
to
the
nearest
meter,
needed
to
mak e
this
tirolienne.
5.
Use
of
the
c osine
E.4918
Consider
the
four
triangles
sho wn
b elo w
:
Determine
the
lengths
of
the
follo wing
segmen ts,
rounded
to
the
nearest
millimeter :
a
[
AB
]
b
[
JL
]
Hints :
Below
is
part
of
the
trigonometric
table
for
cosine.
¸
o
cos
¸
o
¸
o
cos
¸
o
¸
o
cos
¸
¸
o
cos
¸
o
¸
o
cos
¸
o
0
o
1
20
o
0
;
94
40
o
0
;
766
60
o
0
;
5
80
o
0
;
174
5
o
0
;
996
25
o
0
;
906
45
o
0
;
707
65
o
0
;
423
85
o
0
;
087
10
o
0
;
985
30
o
0
;
866
50
o
0
;
643
70
o
0
;
342
90
o
0
15
o
0
;
966
35
o
0
;
819
55
o
0
;
574
75
o
0
;
259
https:/ /c hingmath.fr
chapExoCorrec/9025 sacados/9025 E D F 3 ; 5 cm 75 o J L K 6 ; 5 cm 20 o chapExoCorrec/6440 sacados/6440 A B C 6 cm 33 o G I H 3 cm 65 o chapExoCorrec/9027 sacados/9027 J L K 4 ; 5 cm 40 o E D F 1 ; 5 cm 48 o chapExoCorrec/9020 sacados/9020 10 o chapExoCorrec/4918 sacados/4918 A B C 4 ; 5 cm 20 o J K L 1 ; 5 cm 75 o
G H I 5 cm 25 o D E F 3 ; 5 cm 35 o
4 cm 6 cm 40 o 20 o A B C M N P A B C D E F G H I
E.9026
Consider
the
four
triangles
sho wn
b elo w
:
Determine
the
lengths
of
the
follo wing
segmen ts,
rounded
to
the
nearest
millimeter :
a
[
ED
]
c
[
GI
]
Hint :
Below
is
part
of
the
trigonometric
table
for
cosine.
¸
o
cos
¸
o
¸
o
cos
¸
o
¸
o
cos
¸
¸
o
cos
¸
o
¸
o
cos
¸
o
0
o
1
20
o
0
;
94
40
o
0
;
766
60
o
0
;
5
80
o
0
;
174
5
o
0
;
996
25
o
0
;
906
45
o
0
;
707
65
o
0
;
423
85
o
0
;
087
10
o
0
;
985
30
o
0
;
866
50
o
0
;
643
70
o
0
;
342
90
o
0
15
o
0
;
966
35
o
0
;
819
55
o
0
;
574
75
o
0
;
259
E.1156
Consider
the
t w o
triangles
ABC
and
MN P
shown
b elo w
:
Determine
the
lengths
of
the
follo wing
segmen ts,
rounded
to
the
nearest
millimetre :
a
[
AC
]
b
[
MN
]
6.
Use
of
the
r e cipr o c al
c osine
E.2114
Note:
when
w e
lo ok
at
the
cosine
trigonometric
table,
w e
see
the
cosine
v alues
decreasing
from
1
to
0
:
it
nev er
tak es
the
same
v alue
t wice.
Proposition-definition :
in
a
righ t-angled
triangle,
the
v alue
:
r
=
longueur
of
the
adjacen t
longueur
side
of
the
h yp otén use
of
an
acute
angle
is
uniquely
asso ciated
with
the
measure
¸
of
that
angle.
Note
cos
−
1
(
r
)
the
measure
of
this
angle.
Consider
the
three
righ t-angled
triangles
b elo w
:
1
a
Carry
out,
on
the
figure
ab o v e,
the
measuremen ts
b elo w,
transferring
them
to
the
table
:
AB
AC
BC
DE
DF
EF
GH
GI
HI
b
Giv e
the
v alue
of
the
follo wing
quotien ts
rounded
to
the
nearest
h undredth
:
AC
AB
BC
AB
DF
DE
EF
DE
HI
HG
GI
HG
Indication
:
we
recall
the
extract
from
the
trigonometric
table
b elo w
:
α
cos
¸
α
cos
¸
α
cos
¸
α
cos
¸
α
cos
¸
0
1.000
2
0.999
4
0.998
6
0.995
8
0.990
10
0.985
12
0.978
14
0.970
16
0.961
18
0.951
20
0.940
22
0.927
24
0.914
26
0.899
28
0.883
30
0.866
32
0.848
34
0.829
36
0.809
38
0.788
40
0.766
42
0.743
44
0.719
46
0.695
48
0.669
50
0.643
52
0.616
54
0.588
56
0.559
58
0.530
60
0.500
62
0.469
64
0.438
66
0.407
68
0.375
70
0.342
72
0.309
74
0.276
76
0.242
78
0.208
80
0.174
82
0.139
84
0.105
86
0.070
88
0.035
3
Using
the
trigonometric
table,
giv e
an
appro ximate
v alue
for
eac h
of
the
follo wing
angles
:
BAC
ABC
FD E
FE D
GHI
HGI
https:/ /c hingmath.fr
chapExoCorrec/9026 sacados/9026 G H I 5 cm 25 o D E F 3 ; 5 cm 35 o chapExoCorrec/1156 sacados/1156 4 cm 6 cm 40 o 20 o A B C M N P chapExoCorrec/2114 sacados/2114 A B C D E F G H I
A B C 3.5 cm 4.5 cm G I H 3 cm 4.5 cm E D F 2.5 cm 3.5 cm J L K 3 cm 5.7 cm
A B C D E 5 cm 4 ; 5 cm 2 cm A B C 7 cm 4 cm
E.4931
Below
is
an
excerpt
from
the
trigonometric
table
of
cosines
with
a
step
size
of
2
o
:
α
cos
¸
α
cos
¸
α
cos
¸
α
cos
¸
α
cos
¸
0
1
;
000
2
0
;
999
4
0
;
998
6
0
;
995
8
0
;
990
10
0
;
985
12
0
;
978
14
0
;
970
16
0
;
961
18
0
;
951
20
0
;
940
22
0
;
927
24
0
;
914
26
0
;
899
28
0
;
883
30
0
;
866
32
0
;
848
34
0
;
829
36
0
;
809
38
0
;
788
40
0
;
766
42
0
;
743
44
0
;
719
46
0
;
695
48
0
;
669
50
0
;
643
52
0
;
616
54
0
;
588
56
0
;
559
58
0
;
530
60
0
;
500
62
0
;
469
64
0
;
438
66
0
;
407
68
0
;
375
70
0
;
342
72
0
;
309
74
0
;
276
76
0
;
242
78
0
;
208
80
0
;
174
82
0
;
139
84
0
;
105
86
0
;
070
88
0
;
035
The
figure
b elo w
sho ws
four
triangles
with
measuremen ts
mark ed
on
them
:
Give
the
appro ximate
v alue
of
eac h
angle
to
the
nearest
t w o
degrees
:
a
BAC
c
HGI
E.9028
The
figure
b elo w
sho ws
four
trian- gles
;
measuremen ts
are
plotted
on
it :
Determine
the
measure
of
the
follo wing
angles
rounded
to
the
nearest
ten th
of
a
degree
:
a
∠
DE F
b
∠
LJK
7.
Use
of
c osine
and
inverse
c osine
E.9019
Consider
the
figure
b elo w
where
:
p oin ts
A
,
B
,
D
and
p oin ts
A
,
C
,
E
are
aligned
;
triangles
ABC
and
AED
are
rectangles
at
B
and
E
re-sp ectiv ely .
1
Determine,
to
the
nearest
ten th
of
a
degree,
the
measure
of
the
angle
∠
BAC
.
2
Use
the
previous
question,
to
determine
the
measure
of
segmen t
[
CE
]
rounded
to
the
nearest
millimeter.
E.4932
Consider
a
triangle
ABC
right- angled
C
such
that
:
AC
=
4
cm
;
AB
=
7
cm
1
Determine
the
measure
of
the
angle
∠
CAB
rounded
to
the
ten th
degree.
In
the
remainder
of
the
exercise,
the
rounded
v alue
of
the
angle
∠
CAB
obtained
in
the
previous
question
will
b e
used
:
2
In
this
question,
w e
will
not
use
the
Pythagorean
theo- rem
:
a
Determine
the
measure
of
the
angle
∠
CB A
rounded
to
the
nearest
ten th
of
a
degree.
b
Deriv e
the
length
of
side
[
BC
]
rounded
to
the
nearest
millimeter.
https:/ /c hingmath.fr
chapExoCorrec/4931 sacados/4931 A B C 3.5 cm 4.5 cm G I H 3 cm 4.5 cm chapExoCorrec/9028 sacados/9028 E D F 2.5 cm 3.5 cm J L K 3 cm 5.7 cm chapExoCorrec/9019 sacados/9019
A B C D E 5 cm 4 ; 5 cm 2 cm chapExoCorrec/4932 sacados/4932 A B C 7 cm 4 cm
3 ; 5 cm 2 ; 5 cm 4 cm A B C D O H C S 15 o
A B C 13 k m 5 k m C C O P A B Q 6 cm
E.4935
Consider
the
figure
b elo w
:
The
straigh t
lines
(
AC
)
and
(
BD
)
intersect
at
the
p oin t
O
.
1
a
Determine
the
measure
of
the
angle
∠
BAO
rounded
to
the
nearest
ten th
of
a
degree.
b
Deriv e
the
measure
of
the
angle
∠
CO D
.
2
Determine
the
p erimeter
of
the
triangle
OD C
rounded
to
the
nearest
millimeter.
E.1157
An
explorer
arriv es
in
fron t
of
the
Cheops
p yramid.
He
places
his
measuring
instrumen ts
(theo dolite)
at
p oin t
H
.
Studying
the
p yramid,
he
observ es
that
it
is
a
regular
p yramid :
the
fo ot
C
of
the
heigh t
from
the
v ertex
S
is
also
the
cen ter
of
the
base.
It
also
estimates
the
distance
HC
to
550
m
.
F rom
p oin t
H
to
v ertex
S
,
his
measuring
instru- men ts
rev eal
an
angle
of
15
o
.
Determine
the
measure
of
heigh t
SC
of
the
Pyramid
of
Cheops
rounded
to
the
nearest
metre.
8.
Cosine,
Pythagor e an
the or em
and
Thales
the or em
E.9018
Consider
the
triangle
ABC
right- angled
C
shown
b elo w
:
1
Determine
the
measure
of
segmen t
[
AC
]
.
2
Deduce
the
measure,
to
the
nearest
degree,
of
the
angle
∠
CAB
.
E.5988
Opp osite
is
sho wn
the
righ t-angled
triangle
BP Q
at
B
such
that
:
PB
=6
cm
;
PQ
=8
cm
The
circle
C
is
the
circum- scrib ed
circle
of
the
trian- gle
BP Q
.
W e
construct
the
circle
C
with
cen ter
P
and
passing
through
p oin t
B
.
W e
de- note
A
as
the
p oin t
of
in- tersection
of
circle
C
and
segmen t
[
PQ
]
.
The
aim
of
the
exercise
is
to
determine
an
appro ximate
v alue
for
the
area
of
the
shaded
part.
1
Determine
the
area
of
the
disk
C
rounded
to
the
nearest
ten th
of
cm
2
.
Hint :
we
will
use
:
ı
≈
3.1416
2
a
Determine
the
measure,
rounded
to
the
nearest
ten th
of
a
degree,
of
angle
APB
.
b
Deduce
the
area,
rounded
to
the
nearest
ten th
of
cm
2
,
of
the
angular
sector
of
the
circle
C
defined
b y
the
arc
AB
.
3
Deduce
a
measuremen t,
rounded
to
the
nearest
ten th
of
cm
2
,
of
the
shaded
part.
https:/ /c hingmath.fr
chapExoCorrec/4935 sacados/4935 3 ; 5 cm 2 ; 5 cm 4 cm A B C D O chapExoCorrec/1157 sacados/1157 H C S 15 o chapExoCorrec/9018 sacados/9018 A B C 13 k m 5 k m chapExoCorrec/5988 sacados/5988 C C O P A B Q 6 cm
altitude d’arrivée altitude départ dénivelé angle de p en te A B C Figure 1 Sommet déniv elé seconde étap e déniv elé première étap e Départ D E F G H 3800 m 4100 m 3790 m 12 o Figure 2
O A B M N
E.9016
Pour
moun tain
running,
some
athletes
measure
their
p er- formance
b y
the
ascension
v elo cit y
,
noted
V
a
.
V
a
is
the
quotien t
of
the
difference
in
elev ation
of
the
race,
expressed
in
meters,
b y
the
duration,
expressed
in
hours.
Example:
for
a
gradien t
of
4
500
m
and
a
run
time
of
3
h
:
V
a
=
1
500
m
=
h
Reminder
:
the
altitude
difference
of
the
race
is
the
differ- ence
b et w een
the
altitude
at
the
finish
and
the
altitude
at
the
start.
A
top-lev el
runner
w an ts
to
ac hiev e
an
ascen t
sp eed
of
at
least
1
400
m
=
h
during
his
next
race
The
figure
b elo w
is
not
a
full-scale
represen tation.
The
route
breaks
do wn
in to
t w o
stages
(see
figur e
2)
:
First
step
of
3
800
m
for
a
horizon tal
displacemen t
of
3
790
m
.
Second
stage
of
4.1
km
with
a
slop e
angle
of
appro xi- mately
12
o
.
1
Chec k
that
the
gradien t
of
the
first
stage
is
appro xi- mately
275.5
m
.
2
Ho w
steep
is
the
second
stage?
(we’ll
r ound
to
the
ne ar- est
de cimeter)
3
F rom
the
start,
the
runner
tak es
48
minutes
to
reac h
the
summit.
Do es
the
runner
reac h
his
goal?
9.
Unclassified
exer cises
E.1155
Let
OAB
be
a
righ t
triangle
at
A
.
Con- sider
p oin ts
M
and
N
,
whic h
lie
on
line
segmen ts
[
OA
]
and
[
OB
]
,
resp ectiv ely ,
suc h
that
triangle
OM N
is
a
righ t
triangle
at
M
.
1
Justify
the
follo wing
equalit y :
ON
×
OA
=
OB
×
OM
.
2
a
Using
y our
protractor,
find
the
measure
of
angle
AOB
.
b
T ak e
measuremen ts,
to
the
nearest
millimeter,
on
the
figure
to
complete
the
table
b elo w
:
Segment
[
OA
]
[
OM
]
[
OB
]
[
ON
]
Length
c
Giv e
the
v alues
of
the
ratios,
rounded
to
the
nearest
thousandth
:
OM
ON
;
OA
OB
3
a
What
conjecture
can
b e
made
ab out
the
quotien ts
OM
ON
and
OA
OB
?
b
Using
question
1
,
,
justify
that
the
t w o
quotien ts
OM
ON
and
OA
OB
are
equal.
https:/ /c hingmath.fr
chapExoCorrec/9016 sacados/9016 altitude d’arrivée altitude départ dénivelé angle de p en te A B C Figure 1 Sommet déniv elé seconde étap e déniv elé première étap e Départ D E F G H 3800 m 4100 m 3790 m 12 o Figure 2
chapExoCorrec/1155 sacados/1155 O A B M N