1
In the diagram, AB = BC = 3 cm, DC = 4.5
cm, angle ABC = 90° and angle
ACD = 25°.
D
(a) Calculate the length of AC.
4.24 cm
A
4.5 cm
3 cm
B
25°
3 cm
C
2 The height of a vertical cliff is 450 m. The
angle of elevation from a ship to the top of
the cliff is 23°. The ship is x meters from
the bottom of the cliff.
Calculate the value of x.
1060 m
(3 sig figs)
3
The diagram shows a water tower standing on horizontal
ground. The height of the tower is 26.5 m.
From a point A on the ground the angle of elevation to the
top of the tower is 28°.
Calculate, correct to the nearest meter, the distance x m.
50 m
xm
A
4
In the diagram, AB = BC = 3 cm, DC = 4.5
cm, angle ABC = 90° and angle
ACD = 25°.
(b) Calculate the area of
triangle ACD.
4.03 cm2
D
A
4.5 cm
3 cm
B
25°
3 cm
C
5
A rectangular block of wood with face ABCD leans against
a vertical wall, as shown in the diagram below. AB = 8 cm,
BC = 5 cm and angle BAE = 28°.
Wall
F
C
D
B
E
28º
Ground
A
Find the vertical height of C above the ground.
8.17 cm
6
The diagram shows a cuboid 22.5 cm by 40 cm by 30 cm.
(a) Calculate the length
of AC.
37.5 cm
H
E
G
F
(b) Calculate the size of
angle GAC.
40 cm
46.8°
D
C
30 cm
A
22.5 cm
B
7
In the diagram, PQRS is the square base of a solid right
pyramid with vertex V. The sides of the square are 8cm,
and the height VG is 12cm. M is the midpoint of QR.
Diagram not to scale
(a) Calculate the length of VM.
12.6 cm
(b) Find the angle between the
face VQR and the base of the
pyramid. (angle between VM
and MG) 71.6°
(or 72.2° or 71.5°)
V
VG = 12 cm
P
Q
G
S
8 cm
8 cm
M
R
8
The diagram shows the plan of a playground
with dimensions as shown.
C
Calculate the area of triangle ABC
48 m
117º
A
B
57 m
1220 m2 (3 s.f.)
9
The following diagram shows the rectangular prism
ABCDEFGH. The length is 5 cm, the width is 1 cm,
and the height is 4 cm.
C
Find the length
of CF.
B
H
G
6.48 cm
D
A
E
F
Diagram not to scale
10
The diagram shows a point P, 12.3 m from the base
of a building of height h m. The angle measured to
the top of the building from point P is 63°.
Calculate the height h of the
building. 24.1 m
hm
P 63°
12.3
11 OABCD is a square based pyramid of side 4 cm as
shown in the diagram.
The vertex D is 3 cm directly above X, the centre of
square OABC. M is the midpoint of AB.
D
(a) Calculate the length of DM.
3.61 cm
Diagram
not to scale
(b) Calculate the angle between
DM and XM.
B
C
56.3°
X
M
(or 56.2° or 56.4°)
O
A
In the diagram below ABEF, ABCD and CDFE are all
rectangles. AD = 12cm, DC = 20cm and DF = 5cm.
M is the midpoint of EF and N is the midpoint of CD.
12
E
(a) Calculate the length
of AM 16.4 cm
B
M
(b) Calculate the angle
between AM and AN
17.8°
A
12 cm
F
N
5 cm
D
C
13
Determine the area of:
7.3km
38°
9.4 km
21.1 km2
14 A triangle has sides of length 7cm and
13cm and its area is 42cm2. Find the
size of its included angle.
67.4°
15 In the diagram, AB = BC = 3 cm,
D
DC = 4.5 cm, angle ABC = 90° and
angle ACD = 25°.
A
(c) Calculate the area of
quadrilateral ABCD.
8.53
4.5 cm
cm2
3 cm
B
25°
3 cm
C
• When a 5 foot 4 inch tall person casts a 4
foot 2 inch shadow, what is the angle of
elevation of the sun?
• Steps to the entrance of a school rise a total
of 2 feet. They are to be torn out and
replaced by a wheelchair ramp, inclined at
12°. How long (along the slant) is the
ramp?
The measure of angle CBA is 22°. The
measure of angle DBA is 47°. Find the
length of CA.
D
48 cm
C
B
A
BA is 71.8 cm and so AC is 29.0 cm
• The length of the base of an isosceles
triangle is 72.5 inches and each base angle
has a measure 46.8°. Find the length of
each of the two equal sides of the triangle.
53.0 inches
Homework
• Review Set 10A, pg349
– #1-8
• Review Set 10B, pg351
– #1-7