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Geometry
Pythagorean theorem
2
2
2
. John left Town M at
0600
0600
0600
and travelled towards Town
N
N
N
at a constant speed of
54
k
m
/
h
54 \mathrm{~km} / \mathrm{h}
54
km
/
h
. Ben left Town M,
20
20
20
minutes after John and travelled towards Town N at a constant speed of
63
k
m
/
h
63 \mathrm{~km} / \mathrm{h}
63
km
/
h
. At what time after Ben started will he overtake John on the way?
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1
1
1
. Julianna started from Point
A
A
A
and drove towards Point
B
B
B
at a constant speed of
60
k
m
/
h
60 \mathrm{~km} / \mathrm{h}
60
km
/
h
. Half an hour later, Tom started from Point A and drove along the same route at a constant speed of
80
k
m
/
h
80 \mathrm{~km} / \mathrm{h}
80
km
/
h
. How long after Tom started will he overtake Julianna on the way?
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While painting the side of his house, Jason positioned his ladder so that the top was
16
16
16
feet above the ground, while the bottom was
12
12
12
feet away from the base of the wall. To reach a spot higher up on the house, Jason moved the ladder so that the top was
18
18
18
feet above the ground. How much closer to the house is the bottom of the ladder now? If necessary, round your answer to the nearest tenth.
\newline
____ feet
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A chessboard is one large square made up of
8
8
8
rows of
8
8
8
equal sized smaller squares. Krysta has two chessboards. On one board, the small squares are
2
2
2
inches by
2
2
2
inches. On the other, they are
3
3
3
inches by
3
3
3
inches. How much longer is the diagonal of the larger board than the diagonal of the smaller board? If necessary, round your answer to the nearest tenth.
\newline
____ inches
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How long is the shortest route from Mesa Vista to Gibbs using the roads shown?
\newline
\newline
If necessary, round your answer to the nearest tenth.
\newline
\newline
_
_
_
_
\_\_\_\_
____
miles
\newline
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Chad is decorating a rectangular ballroom ceiling with decorative lights. Beginning in a corner, Chad strings the lights along the length of the ceiling, a distance of
55
55
55
feet. Next, Chad strings the lights along the width of the ceiling, a distance of
48
48
48
feet. Then Chad strings the lights straight back to the original corner. At this point, how many feet of lights has Chad used?
\newline
If necessary, round your answer to the nearest tenth.
\newline
____ feet
\newline
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In Rosewood City, the library is
6.5
6.5
6.5
miles due south of the courthouse and
3.4
3.4
3.4
miles due west of the community swimming pool. What is the distance between the courthouse and the community swimming pool?
\newline
If necessary, round your answer to the nearest tenth.
\newline
____ miles
\newline
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Rachel is sitting in a tree
15
15
15
feet above the ground. A minute ago, she spotted a skunk
40
40
40
feet from the base of the tree walking closer to her. Now, the skunk is
20
20
20
feet from the base of the tree. The diagonal line from Rachel to the skunk is the distance between them. How much closer is the skunk to Rachel now than it was a minute ago?
\newline
If necessary, round your answer to the nearest tenth.
\newline
_
_
_
_
\_\_\_\_
____
feet
\newline
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How long is the shortest route from McLain to Austinburg using the roads shown?
\newline
\newline
If necessary, round your answer to the nearest tenth.
\newline
\newline
_
_
_
_
\_\_\_\_
____
miles
\newline
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Brenna is going to swim the length of her rectangular swimming pool. The width of the pool is
36
36
36
feet, and the diagonal distance from one corner to the opposite corner is
60
60
60
feet. What is the length of the pool?
\newline
If necessary, round your answer to the nearest tenth.
\newline
\newline
_
_
_
_
\_\_\_\_
____
feet
\newline
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The Island Loop Ferry takes the same route multiple times a day. It starts at the port of Seabreeze Village and travels due south for
8
8
8
miles to the town of Oceanview. From there, it travels due east for
15
15
15
miles to Portlandville. Finally, it makes a straight-line journey back to Seabreeze Village. If the ferry can travel
5
5
5
miles on a gallon of fuel, how many gallons does the ferry use to complete the route one time? If necessary, round your answer to the nearest tenth.
\newline
____ gallons
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Rose is building a slide for her kids. The ladder is
8
8
8
feet tall and the slide is
17
17
17
feet long. What is the distance between the ladder and the bottom of the slide?
\newline
_
_
_
_
\_\_\_\_
____
feet
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Tim likes to skate at a candy store that is due south of his school and due west of his favorite ice cream parlor. If the candy store is \(12\) kilometers from his school and the straight-line distance between the school and the ice cream parlor is \(13\) kilometers, how far is the candy store from the ice cream parlor?
\newline
____________Kilometers
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X
\mathrm{X}
X
is a point inside triangle
P
Q
R
\mathrm{PQR}
PQR
. It is
3
c
m
3 \mathrm{~cm}
3
cm
from
P
\mathrm{P}
P
, and
4
c
m
4 \mathrm{~cm}
4
cm
from
Q
Q
Q
. How far is
X
X
X
from
R
R
R
?
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The first order of operations rule states: All
\qquad
are done first, starting from the left and working to the right.
\newline
Click on your answer below:
\newline
A. additions
\newline
B. subtractions
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Find the length of the third side. If necessary, round to the nearest tenth.
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Question
\newline
Watch Video
\newline
Show Examples
\newline
Find the Perimeter of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenths place.
\newline
Answer
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9
9
9
: R
3
3
3
: A lighthouse is east of a sailboat. The sailboat's dock is
30
k
m
30 \mathrm{~km}
30
km
south of the lighthouse. The captain measures the angle between the lighthouse and the dock and finds it to be
40
40
40
degrees. How far is the sailboat from the dock? Round to the nearest whole
k
m
\mathrm{km}
km
.
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Find the length of the third side. If necessary, round to the nearest tenth.
14
14
14
10
10
10
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What is the length of the missing leg? If necessary, round to the nearest tenth.
\newline
a
=
a=
a
=
\newline
□
\square
□
yards
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Jillian is a firefighter. She stands at an observation window
85
85
85
ft above the ground. From a distance, she spots a fire! She takes a reading -- and she sees that the angle of depression is
2
8
∘
28^\circ
2
8
∘
. To the nearest tenth of a foot, how far away from the base of the tower is the fire?
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A boat is heading towards a lighthouse, whose beacon-light is
139
139
139
feet above the water. The boat's crew measures the angle of elevation to the beacon,
1
1
∘
11^{\circ}
1
1
∘
. What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
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Kaj is flying a kite, holding her hands a distance of
3
3
3
.
5
5
5
feet above the ground and letting all the kite's string play out. She measures the angle of elevation from her hand to the kite to be
3
3
∘
33^{\circ}
3
3
∘
. If the string from the kite to her hand is
75
75
75
feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
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Tamika wants to use a sheet of fiberboard
19
19
19
inches long to create a skateboard ramp with a
2
0
∘
20^{\circ}
2
0
∘
angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch ifnecessary.
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From the observation deck of a skyscraper, Rahul measures a
4
8
∘
48^{\circ}
4
8
∘
angle of depression to a ship in the harbor below. If the observation deck is
1093
1093
1093
feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
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Question
\newline
Show Examples
\newline
From the observation deck of a skyscraper, Bentley measures a
4
8
∘
48^{\circ}
4
8
∘
angle of depression to a ship in the harbor below. If the observation deck is
969
969
969
feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
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The length of chord of a circle is
22
cm
22\,\text{cm}
22
cm
and the perpendicular distance between the centre and the chord is
60
cm
60\,\text{cm}
60
cm
. Find the radius of the circle.
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A
40
40
40
foot ladder is set against the side of a house so that it reaches up
24
24
24
feet. If Lily grabs the ladder at its base and pulls it
4
4
4
feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not
20
f
t
20 \mathrm{ft}
20
ft
.) Round to the nearest tenth of a foot.
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Question
\newline
Watch Video
\newline
Show Examples
\newline
A
40
40
40
foot ladder is set against the side of a house so that it reaches up
24
24
24
feet. If Lily grabs the ladder at its base and pulls it
4
4
4
feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not
20
f
t
20 \mathrm{ft}
20
ft
.) Round to the nearest tenth of a foot.
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In an A-frame house, a bullet is found embedded at a point
8
f
t
8 \mathrm{ft}
8
ft
up the sloped wall. If it was fired at a
3
0
∘
30^{\circ}
3
0
∘
angle with the horizontal, how far from the base of the wall was the gun fired?
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A water halloon is being launched into the air at a
7
3
∘
73^{\circ}
7
3
∘
angle of elevation from the ground. The water balloon reaches a height of
30
30
30
feet directly above your head. How far from you was the water balloon launched?
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5
5
5
. A water balloon is being launched into the air at a
7
3
∘
73^{\circ}
7
3
∘
angle of elevation from the ground. The water balloon reaches a height of
30
30
30
feet directly above your head. How far from you was the water balloon launched?
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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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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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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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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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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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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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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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