further maths questions
pul0001
weeeks_9_and_10.docxProblem Solving Questions 7 to 14 (Copy out the diagram)
2. Children using the swing, shown below find that if they swing high enough, they will see over the fence. The swing is 0.9 metres above the ground originally.
The swing makes an angle of 62º when it moves from position A to position C.
B
A
C
0.9 m
2.4 m
x
620
2.4 m
ground level
Find the vertical distance x above the ground after the swing moves through 62º?
Ans. ???
270
390
3. A five-metre ladder leans against a wall making an angle of 27º. It slides down making an angle of 39º. How far along the horizontal ground has it moved?
Ans. 19 degrees
9. Trish is working out the height of a communications tower. From point A she takes a sighting of the top of the tower. She then moves 100 metres to point B and takes another sighting.
A
B
850
300
100 m
Height of tower
CTB
HCTB
Use the information to calculate the height of the tower, to the nearest metre.
Ans. 55
10. Find angles B and C. Are there two possible triangles? (Hint: Refer to the ambiguity test for sine rule, page 14)
B
A
C
450
b = 6
a = 5
Ans. angle B is 70 degree and C is 65 degree
11. A vertical mast is secured from its top by straight cables 200 m long fixed at the ground. The cables make angles of 66º with the ground. What is the height of the mast?
(As part of your solution, draw a large labelled diagram and cross-reference it to your working.)
Ans. ?????? A pendulum swings from the vertical through
an angle of 15º on each side of the vertical.
If the pendulum is 90 cm long, what is the
Distance x cm between its highest and lowest points?
Copy out the diagram given and cross-reference
it to your working.
Ans. 6 cm
12. A and B are two points on a coastline. They are 1070 m apart; C is a point at sea.
The angles CAB and CBA have magnitudes of 74º and 69º, respectively.
Find the distance of C from A.
Draw a large labelled diagram and cross-reference it to your working.
Ans. ????
13. In the diagram shown, find the length of
(a) AX
(b) AY
Copy out the diagram given and cross-reference it to your working.
Ans. a is 135 , b is 35
WEEK 10
10. The points M, N and P form the vertices of a triangular course for a yacht race.
MN = MP = 4 km. The bearing of N from M is 070°. The bearing of P from M is 180°
Three people perform different calculations to determine the length of NP in kilometres.
Shelley NP = 2 × 4 × cos 35°
The correct length of NP would be found by
A. Graeme only.
B. Tran only.
C. Graeme and Shelley only.
D. Graeme and Tran only.
E. Graeme, Shelley and Tran. [VCAA Exam 1, 2007]
Ans. D
Part B Written answer questions
All relevant workings must be shown clearly in your responses.
1. A farmer has his house built near a river.The house, H, is 780 metres from the pier, P, and 325 metres from the swimming platform, S, shown in the diagram below.Beside the river are two paddocks, PHS and FHS as shown.
(a) Find the area of each paddock
Area of SHP = ½ * 325 * 780 = 126750 sq m
(b)
Find the length, FH, in metres, correct to one decimal place.
Ans. a is 76050000 , b is ?? , c is 325
2. Find the areas of the following triangles, correct to two decimal places,
using the most appropriate method.
(a) (b)
(c)
a) Area of triangle = ½*a*b*sinC
c^2 = a^2 + b^2 – 2ab*cosC
c = 15.47
so we get
area = ½ * 20 * 15 *sin (15.47)
= 35.35
b) First find side x/sin 31 = 51/sin 23
x = 51*sin31/sin 23
x = 24.35
third angle = 180 – 31 – 23 = 126
area = ½*a*b*sinC = ½ * 52*35.35*sin(126)
area = 303.29
c) Finding angle c
Cos C = (13^2 + 24^2 – 19^2 )/ ( 2*13*24) = 0.90
Area = ½*a*b*sinC
= ½ * 13*24*sin(0.900
= 121.68
3. The area of a triangle ABC is 6 cm2. AB = 3 cm and AC = 5 cm.
(a) Find two possible values for the magnitude of angle BAC
(b) Find two possible lengths for BC.
Ans. a 15 and 18 , b is 15 , 20
4. Find the total area of the figure on the right.
Clearly show all of your working.
Ans. 12m
o
o
4sin110
sin35
´
S
F
H
P
Swimming platform
Pier
River
House
780 m
325 m
155 m
S
F
H
P
Swimming platform
Pier
River
House
780 m
325 m
155 m
o
16 + 16 2 × 4 × 4 × cos 110
-
