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I need the following attached file to be completed.
it has around 3 pages of multiple choice/short answer questions on geonometry and trig. needs to be completed within 1 hour of this post and i will pay $35 if someone can do it.
Problem 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 m
etres 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.
Graeme
NP =
Shelley
NP = 2 × 4 × cos 35°
Tran
NP
=
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
–
ProblemSolving 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.
Find the vertical distance x above the ground after the swing moves through 62º?
Ans. ???
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
C
T
B
A
C
0.9 m
2.4 m
x
620
2.4 m
ground level
270
390
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)
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. ??????
B
A C
450
b = 6
a = 5
H
C
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.
Graeme NP = o16 + 16 2 × 4 × 4 × cos 110−
Shelley NP = 2 × 4 × cos 35°
Tran NP=
o
o
4 sin110
sin35
×
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
ProblemSolving 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.
Find the vertical distance x above the ground after the swing moves through 62º?
2. height of B from ground = 2.4+0.9 = 3.3 m
height of C from ground = 3.3 – 2.4 cos 62 = 2.173
3. 5 sin 39 – 5 sin 27 = 5 (sin 39 – sin 27) = 5(0.17533)
=0.8766 m
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?
19 degrees
B
A
C
0.9 m
2.4 m
x
620
2.4 m
ground level
270
390
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.
Use the information to calculate the height of the tower, to the nearest metre.
height of tower = h and distance of B from tower = x
h/100+x = tan 30 h/x = tan 85 x = h/tan 85 h tan 30 = 100 +(h/tan 85)
h(tan 30 – 1/tan 85) = 100 h (1.732 – 0.08749) = 100 h = 60.80 meter
10. Find angles B and C. Are there two possible triangles? (Hint: Refer to the ambiguity test
for sine rule, page 14)
a./sinA=b/sinB 5/sin 45 = 6/sin B
sin B = 0.848 B = 58 degree angle C = 180-A-B
= 180-45-58 = 77 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?
A B
850
300
100 m
Height of tower
B
A C
450
b = 6
a = 5
C
T
B
H
C
T
B
(As part of your solution, draw a large labelled diagram and
cross-reference it to your
working.)
the difference between the highest point of pendulum and lowest point
= 90 – 90 cos 15 = 90(1- cos 15)
height of the mast = 200 sin 66 = 200 *0.9135 = 182.7 m
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.
the angle ACB = 180 – 74-69 = 37 degree distance of c from a will be
equal to b b/sinB = c/sinC b = c sinB/sinC
= 1070 sin69/sin 37
= 1070 * 0.9335/0.6018 = 1659.72 meter
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.
50/sin 40 = AX/sin 20
AX = 50 sin 20/sin 40 = 26.6
AY/sin 109 = 50/sin 39 Ay = 50 sin 109/sin 39
= 75.12
AC
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.
Graeme NP = o16 + 16 2 × 4 × 4 × cos 110−
Shelley NP = 2 × 4 × cos 35°
Tran NP=
o
o
4 sin110
sin35
×
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.
PS = √7802+3252 = 845
(a) Find the area of each paddock
(b) Area of PHS = 1⁄2 *780*325 = 126750 m2 area of FSH = area of
PHF – area of PHS
(c)
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)
S F
H
P
Swimming platform
Pier
River
House
780 m
325 m
155 m
(a). area of triangle = 1⁄2 xy sinZ = 1⁄2 15*20*sin 50 = 114.90 cm2
(b) 52/sin 23 = x/ sin 31 x = 68.54
area of triangle =1⁄2 52*68.54 * sin (180-23-31) = 1441.70 mm2
(c) s = 13+24+19/2 = 28 using hero’s formula
area = √ 28 15*4*9 = 122.963
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.
(a) 1⁄2 3*5* sinA = 6 sin A = 12/15
= 4/5 A=sin-1 0.8
A = 53 degree value of angle BAC = 53 degree
with two arms as 3 and 5 and an angle 53 degree it will result in a
triangle with one angle 90 degree and other as 37 degree and by
Pythagoras theorem BC = √ 25-9 = 4
4. Find the total area of the figure on the right.
Clearly show all of your working.
area of the figure = 1⁄2* 13 cos 70*13 sin 70 +5*13 sin 70 =
27.16+61.08 = 88.24
