– 12 –
8.
m15/5/matsd/sP1/eng/tZ2/XX
ˆ is 55 and the length of AM
The diagram shows a triangle ABC. The size of angle CAB
is 10 m, where M is the midpoint of AB. Triangle CMB is isosceles with CM = MB .
!oequ9€
+
C
't
gTi8oa
¥
ay
10
Om
MW
diagram not to scale
18°F
na
55
A
nm
'
B
midpoint
(a)
Write down the length of MB.
(b)
ˆ .
Find the size of angle CMB
(c)
Find the length of CB.
Working:
CAA
(b)
(c)
IOM
rule
sin
cos
or
rule
180-110=70
-
CAB
180-70=116
-71=350
2
a
X
sixties
XSin35=lOsinu0
Jin
Henry
×=(OsinVO
=
Answers:
35
16.383
.
.
TE
X=
16.4
m
-
20EP12
.
(a)
. . . . . . .tom
.........................
(b)
. . . . . . . 110°
.........................
(c)
. . . . . . . .16.4mi
........................
[1]
[2]
[3]
– 16 –
12.
m15/5/matsd/sP1/eng/tZ2/XX
In the following diagram, ABCD is the square base of a right pyramid with vertex V. The
centre of the base is O. The diagonal of the base, AC, is 8 cm long. The sloping edges are
10 cm long.
V
diagram not to scale
not
"
:
sjn
To
66.4
25J
=
×
=
10
sin
66.4
10 cm
May
¥498
C
mock
D
B
O
8 cm
A
(a)
Write down the length of AO.
[1]
(b)
Find the size of the angle that the sloping edge VA makes with the base of
the pyramid.
[2]
Hence, or otherwise, find the area of the triangle CAV.
[3]
r.mg#+AprillJ
(c)
Working:
x=adj_
4
=
10
hyp
'
(b)
(c)
D=
'
a
42
bh
+
1,4g
cos
102×2
102
x=
-
42
#
9.16515
X=
To
.
66.4
=
=
↳ =¥4€=
66
a
...
C
=
+×2
=
°
4218
36.64
36.7
cm2
20EP16
Answers:
(a) . . . . . .4cm
...........................
°
(b) . . . . . . .66.4
..........................
2
cm
(c) . . . . . . .36.7
..........................