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Geometry
Pythagorean theorem
The side length of an equilateral triangle is
5
5
5
centimeters. Find the length of an altitude. Round your answer to the nearest tenth.
\newline
The length of the altitude is about
□
\square
□
centimeters.
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2
2
2
. Tom built a fence around his rectangular shaped pool. The posts are
2
2
2
metres apart. There are
4
4
4
posts along the width and
8
8
8
posts along the length. How many posts does Tom need and what are the dimensions of the fence?
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2
2
2
. Aaron starts walking at a rate of
3
m
i
/
h
3 \mathrm{mi} / \mathrm{h}
3
mi
/
h
on a road toward a store
10
m
i
10 \mathrm{mi}
10
mi
away. Zhang leaves the store when Aaron starts walking, and he walks toward Aaron along the same road at
2
2
2
m
i
/
h
\mathrm{mi} / \mathrm{h}
mi
/
h
. How many hours will pass before they meet?
\newline
A
1.5
h
1.5 \mathrm{~h}
1.5
h
\newline
C
2
h
2 \mathrm{~h}
2
h
\newline
B
10
h
10 \mathrm{~h}
10
h
\newline
D
3
h
3 \mathrm{~h}
3
h
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5
5
5
.
\newline
Ch.
3
3
3
-Acute Triangle Trigonometry
\newline
25
25
25
Mar
2024
2024
2024
\newline
nearest tenth of a metre?
\newline
How far is the point on the ground from the base of the building, to How tall is the crane?
\newline
x
=
27
x=27
x
=
27
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Uhe o dhoming triangle and o stralghtedge to drow a line segment poncllit to ZD throwgh point
Y
Y
Y
.
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Isabella is playing with her yo-yo. The vertical distance
Y
Y
Y
(in
c
m
\mathrm{cm}
cm
) between the yo-yo and her hand
t
t
t
seconds after she first spins it out is modeled by the following function. Here,
t
t
t
is in radians.
\newline
Y
(
t
)
=
40
cos
(
2
π
3
t
)
−
71
Y(t)=40 \cos \left(\frac{2 \pi}{3} t\right)-71
Y
(
t
)
=
40
cos
(
3
2
π
t
)
−
71
\newline
How long does it take the yo-yo to fall all the way down from its peak, and then rise up to a vertical distance of
−
80
c
m
-80 \mathrm{~cm}
−
80
cm
?
\newline
Round your final answer to the nearest tenth of a second.
\newline
□
\square
□
seconds
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Bilal's fishing line was on a spool with a radius of
4
c
m
4 \mathrm{~cm}
4
cm
. Suddenly, a fish pulled on the line, and the spool spun
16
16
16
times before Bilal began to reel in the fish.
\newline
What is the distance the fish pulled the fishing line?
\newline
Round your answer to the nearest
c
m
\mathrm{cm}
cm
.
\newline
□
\square
□
c
m
\mathrm{cm}
cm
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You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey. The tire's diameter is
1
1
1
meter, and it made
8000
8000
8000
rotations during the trip.
\newline
How far did the bus travel?
\newline
Round your answer to the nearest meter.
\newline
□
\square
□
meters
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The second hand on a clock is
8
c
m
8 \mathrm{~cm}
8
cm
long.
\newline
What is the distance the tip of the second hand travels in
10
10
10
minutes?
\newline
Round your answer to the nearest
c
m
\mathrm{cm}
cm
.
\newline
□
\square
□
c
m
\mathrm{cm}
cm
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Aliaa is skating down a ramp. The wheels on her skateboard have diameters of
60
m
m
60 \mathrm{~mm}
60
mm
.
\newline
What is the distance Aliaa travels when her skateboard wheels make
20
20
20
revolutions?
\newline
Round your answer to the nearest
m
m
\mathrm{mm}
mm
.
\newline
□
\square
□
m
m
\mathrm{mm}
mm
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A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of
30
c
m
30 \mathrm{~cm}
30
cm
, and the bicycle wheel makes
3
3
3
full rotations before stopping.
\newline
How long is the trace of water left on the floor?
\newline
Round your answer to the nearest
c
m
\mathrm{cm}
cm
.
\newline
□
\square
□
cm
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A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is
10
meters
10\,\text{meters}
10
meters
and the distance between the gopher's holes is
26
meters
26\,\text{meters}
26
meters
. How wide is the yard?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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Beth ran the width of a field, a distance of
35
35
35
yards. Then she ran the length of the field, a distance of
84
84
84
yards. Finally, she ran diagonally across it to get back to her starting point. How far did Beth run?
\newline
_
_
_
_
\_\_\_\_
____
yards
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On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is
40
40
40
feet and the distance between the tire swing and the monkey bars is
50
50
50
feet, how far is the slide from the monkey bars?
\newline
_
_
_
_
_
_
_
\_\_\_\_\_\_\_
_______
feet
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Julian is creating a stained glass windowpane that will be
72
72
72
centimeters by
21
21
21
centimeters. To make the rectangular windowpane, Julian fuses together two triangles of colored glass. What is the perimeter of one triangle?
\newline
_____ centimeters
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Patty climbs a
40
40
40
-foot tower to ride a straight water slide. After landing in the splash pool, she walks
42
42
42
feet back to the base of the tower. How far did she travel in all?
\newline
_
_
_
_
\_\_\_\_
____
feet
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A mouse has made holes in opposite corners of a rectangular kitchen. Starting from its hole in the northwest corner, the mouse scurries
20
20
20
feet along the length of the kitchen to reach a piece of cheese in the southwest corner. Then the mouse scurries
15
15
15
feet along the width of the kitchen to its other hole in the southeast corner. Finally the mouse scurries back to the first hole. What is the total distance the mouse scurries?
\newline
_____ feet
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An envelope measures
9
9
9
centimeters by
40
40
40
centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?
\newline
_____ centimeters
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Polly measured the floor of her storage unit, which is rectangular. It is
14
14
14
feet wide and
50
50
50
feet from one corner to the opposite corner. How long is the storage unit?
\newline
_
_
_
_
\_\_\_\_
____
feet
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Damon is playing on the slide. Over and over, he climbs the
8
8
8
-foot ladder, goes down the slide, and walks
6
6
6
feet to get back to the ladder. How far does Damon travel each time he repeats this process?
\newline
_____ feet
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Sidney is deep-sea diving with Aiden, who is to the south of her. A fish emerges from a hole to the east of Aiden. The fish swims
24
meters
24\,\text{meters}
24
meters
to Aiden and then swims
10
meters
10\,\text{meters}
10
meters
to Sidney. The fish then swims back to its hole and disappears. How far did the fish travel in all?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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Three ballet dancers are positioned on stage. Ruth is
15
15
15
feet straight behind Pablo and
20
20
20
feet directly left of Chase. When the music begins, Ruth twirls to Chase's position, then leaps to Pablo's position, and finally walks back to her original position. How far did Ruth travel?
\newline
_____ feet
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A jogger running around a rectangular park takes a shortcut back to her car by jogging from one corner of the park to the diagonally opposite corner. If the park is
60
yards
60\,\text{yards}
60
yards
by
45
yards
45\,\text{yards}
45
yards
, how far is the shortcut?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
yards
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Three baseball players are playing catch. Eli is
15
15
15
feet south of Alexandra and
20
20
20
feet west of Matt. How far does Alexandra need to throw the ball to get it to Matt?
\newline
_
_
_
_
\_\_\_\_
____
feet
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Alexandra is going to swim the length of her swimming pool. The width of her pool is
21
21
21
meters and the diagonal distance from one corner to the opposite corner is
29
29
29
meters. How far will Alexandra swim when she swims the length?
\newline
_____ meters
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Three students are sitting on a school bus. Billy is
4
meters
4\,\text{meters}
4
meters
directly behind Sidney and
3
meters
3\,\text{meters}
3
meters
directly left of Gordon. Billy makes a paper airplane and throws it to Sidney. Sidney throws the airplane to Gordon, who throws it back to Billy. How far has the paper airplane traveled?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
meters
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(
4
4
4
) An airplane is flying directly over your house. The distance between your house and the airport is
12
12
12
miles. The altitude of the airplane is
4
4
4
miles. Determine the distance between the airplane and the airport to the nearest hundredth of a mile.
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0
0
0
The diagonal length of a square window is
40
40
40
centimeters. Find the area of th window.
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8
8
8
. In a recreation park, a children's slide is
27
f
t
27 \mathrm{ft}
27
ft
long and makes an angle of
3
9
∘
39^{\circ}
3
9
∘
with the ground. Its top is reached by a ladder
18
f
t
18 \mathrm{ft}
18
ft
long. What is the angle of inclination of the ladder? Round to the nearest tenth of a degree.
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Find the area of the shaded sector. Round to the nearest tenth
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⋆
\star
⋆
SHORT RESPONSE The point of no return in aviation is the farthest point to which a plane can fly and still have enough fuel to return to its starting place or to fly to an alternative landing destination. After a plane passes the point of no return, it must fly to its planned destination. The distance between consecutive grid lines represents
50
50
50
nautical miles.
\newline
The flight path of a plane is from airport A to airport B. The plane is currently at the midpoint of the flight path. How far away is the plane from airport A? Round your answer to the nearest nautical mile.
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A street light is mounted on a pole. A
6
6
6
-foot-tall man is standing on the street a short distance from the pole, casting a shadow. The angle of elevation from the tip of the man’s shadow to the top of his head of
2
8
∘
28^\circ
2
8
∘
. A
6
6
6
-foot-tall woman is standing on the same street on the opposite side of the pole from the man. The angle of elevation from the tip of her shadow to the top of her head is
2
8
∘
28^\circ
2
8
∘
. If the man and woman are
20
20
20
feet apart, how far is the street light from the tip of the shadow of each person? Round the distance to the nearest tenth of a foot.
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3
4
\frac{3}{4}
4
3
of the length of curtain
a
a
a
is equal to
5
6
\frac{5}{6}
6
5
the length of curtain
b
b
b
. curtain
b
b
b
is
60
cm
60\,\text{cm}
60
cm
shorter than curtain
a
a
a
. what is the length of curtain
a
a
a
?
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Paul and Peter left their home at
5
5
5
o'clock to go to the market if Peter travelled at a constant speed of
100
m/min
100\,\text{m/min}
100
m/min
and Paul at
60
m/min
60\,\text{m/min}
60
m/min
. Peter after arriving at the market spent
5
5
5
minutes sitting around before finally going back at the same route to help Paul if they met at
5
5
5
o'clock to
6
6
6
o'clock. Whats the distance between their house and the market
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A children's toy seller will sell his toys to village
B
B
B
, he walks from village
A
A
A
south for
12
12
12
km then east for
5
5
5
km and still walks east then south for
6
6
6
km and arrives at village
B
B
B
Calculate the closest distance between village
A
A
A
and village
B
B
B
!
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Solve for
x
x
x
. Round to the nearest tenth of a degree, if necessary.
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The edges of a cube are
5
5
5
centimeters each and the diagonal of a face is approximately
7
7
7
centimeters. What is the approximate area of the cross section passing through the diagonals of opposite faces of this cube?
\newline
A.
12
12
12
square centimeters
\newline
B.
25
25
25
square centimeters
\newline
C.
35
35
35
square centimeters
\newline
D.
49
49
49
square centimeters
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Paul is building a deck within a corner of his house that measures
25
25
25
by
30
30
30
feet. How long will the deck extend from one corner of his house to the other, rounded to the nearest foot?
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A chandelier is suspended from the ceiling by two chains. One chain is
40
cm
40\,\text{cm}
40
cm
long and forms a
5
5
∘
55^\circ
5
5
∘
angle with the ceiling. The other is
59
cm
59\,\text{cm}
59
cm
long. To the nearest degree, what angle do the two chains make where they connect to the chandelier?
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A teacher started her work day at
7
:
00
7:00
7
:
00
am and stopped it at
3
:
35
3:35
3
:
35
pm. But in between she had a
45
45
45
minute lunch break, and another break of
20
20
20
minutes. How many hours/ minutes did she actually work
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A bowler throws a cricket ball at a speed of
36
k
m
/
h
r
36 \mathrm{~km} / \mathrm{hr}
36
km
/
hr
. How long does this ball take to travel a distance of
20
20
20
metres to reach the batsman?
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If you place a
24
24
24
-foot ladder against the top of a
20
20
20
-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
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A frog is in a
40
m
40\,\text{m}
40
m
deep place. Each day, the frog climbs
3
m
3\,\text{m}
3
m
, but falls back
1
m
1\,\text{m}
1
m
at night. How many days will it take to get out?
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Roselyn is driving to visit her family, who live
150
150
150
kilometers away. Her average speed is
60
60
60
kilometers per hour. The car's tank has
20
20
20
liters of fuel at the beginning of the drive, and its fuel efficiency is
6
6
6
kilometers per liter. Fuel costs
0.60
0.60
0.60
dollars per liter. How long can Roselyn drive before she runs out of fuel?
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You are on the roof of a building and see a friend standing
190
190
190
meters away from the base of a building. The angle of depression to your friend is
2
8
∘
28^{\circ}
2
8
∘
. How far below are they?
\newline
They are
□
\square
□
meters below you (round your answer to three decimal places)
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In Belleville, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is
6.6
6.6
6.6
kilometres and the distance between the courthouse and the city pool is
8.2
8.2
8.2
kilometres, how far is the library from the community pool? If necessary, round to the nearest tenth.
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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box
22
22
22
feet up. The ladder makes an angle of
6
6
∘
66^\circ
6
6
∘
with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
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Alice is driving north at
80
k
m
/
h
80 \mathrm{~km} / \mathrm{h}
80
km
/
h
and Bob is driving east at
50
k
m
/
h
50 \mathrm{~km} / \mathrm{h}
50
km
/
h
. Both cars are approaching the intersection of the two roads. At what rate is the distance between the two cars decreasing when Alice's car is
0.5
k
m
0.5 \mathrm{~km}
0.5
km
from the intersection and Bob's car is
0.8
k
m
0.8 \mathrm{~km}
0.8
km
from the intersection?
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A car travels at
54
km/h
54\,\text{km/h}
54
km/h
for first
20
s
20\,\text{s}
20
s
,
36
km/h
36\,\text{km/h}
36
km/h
for next
30
s
30\,\text{s}
30
s
and finally
18
km/h
18\,\text{km/h}
18
km/h
for next
10
s
10\,\text{s}
10
s
. Find its average speed.
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Luis is flying a kite, holding his hands a distance of
3.75
3.75
3.75
feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be
3
5
∘
35^\circ
3
5
∘
. If the string from the kite to his hand is
140
140
140
feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
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