Trigonometry
E
A
a
b
c
d
F
D
N
M
B
C
X
Write down the lengths of EN and MN.
Find the angle between EM and the plane ABCD.
Calculate the length NC.
Find the angle which the line EC makes with the plane ABCD.
TASK 6.9
A
Remember
c
B
a = b = c
sin A
sin B
sin C
b
sin A = sin B = sin C
a
c
b
or
C
a
Use a calculator and give all answers to 3 significant figures.
!!
Find the value of each letter in Questions 1 to 6
!
1.
!
2.
a
83°
12 cm
74°
59°
42°
!
!
4.
5.
9·4 cm
72°
42°
f
!
3.
b
6·4 cm
88°
19 cm
e
81°
c
!
6.
5·4 cm
63° d
! OUP: this may be reproduced for class use solely for the purchaser’s institute
4·9 cm
7 cm
39°
h
16 cm
g
10
Trigonometry
7. In triangle KLM, KM = 6·8 cm, the angle KLM = 78" and
the angle MKL = 34".
Find the perimeter of triangle KLM.
8. Maddlestone is 28 km due north of Kenton. Howick is on a bearing
of 137" from Maddlestone and Howick is on a bearing of 067" from
Kenton. Find the shortest distance from Kenton to Howick.
TASK 6.10
Remember
B
c
A
area = 1 ab sin —C
2
a
C
b
Use a calculator and give all answers to 3 significant figures when appropriate.
!!
!
Find the value of each letter in Questions 1 to 3
!
1.
36°
5·9 cm
7·4 cm
2.
b
a
8·2 cm
5·3 cm
e
c
f
!
3.
d
g
i
h
76°
6·2 cm
69°
12·8 cm
4. In triangle ABC, AB = 15·1 cm, BC = 29·7 cm and AC = 19·6 cm.
Find the area of triangle ABC.
5. Balloon A travels 15 km on a bearing of 029".
Balloon B travels 39 km on a bearing of 043".
a How far apart are the balloons now?
b On what bearing would balloon A have to travel
in order to reach the position of balloon B?
Q
6. If the area of triangle PRS is 127 cm2,
find the area of triangle PQR.
P
12 cm
11·9 cm
24°
R
23 cm
S
! OUP: this may be reproduced for class use solely for the purchaser’s institute
11
Trigonometry
7. Hanif walks 6 km on a bearing of 159" then 9 km on a bearing of 252". On what bearing
must Hanif walk to return to his starting point and how much further must he walk?
TASK 6.11
Remember
A
b
c
B
a2 = b2 + c2 " 2bc cos —A
a
or
2
2
2
cos —A = b + c " a
2bc
C
Use a calculator and give all answers to 3 significant figures.
!!
Find the value of each letter in Questions 1 to 3
!
1.
8 cm
75°
a
!
2.
14 cm
!
3.
25 cm
b
23°
9 cm
17 cm
11 cm
c
9 cm
4. In triangle PQR, PQ = 32 cm, PR = 28 cm and QR = 21 cm.
Find the size of angle QPR.
5. A boat sails due north for 41 km then travels on a bearing of 218" for 23 km. The
boat then sails back to its starting position. Find the total distance travelled by
the boat.
6. Yaco is 14 km due east of Davina. Yaco walks on a bearing of x" and Davina walks
on a bearing of y". They meet at a more southerly point when Yaco has walked
7 km and Davina has walked 10 km. Find x and y.
B
7. Find the perimeter of triangle ABC.
52°
9 cm
8 cm
A
! OUP: this may be reproduced for class use solely for the purchaser’s institute
109°
D
5 cm
C
12