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Pythagorean theorem
25
25
25
.A hockey net is
4.8768
m
4.8768 \mathrm{~m}
4.8768
m
wide. A player shoots from a point where the puck is
6
m
6 \mathrm{~m}
6
m
from one goal post and
4.5
m
4.5 \mathrm{~m}
4.5
m
from the other. Within what angle must he shoot? (
3
3
3
marks)
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limal sold.
\newline
Q. Carrer faveled
95
95
95
mives from sarteil to tantel field by far for part of the way and then Chit mal train nar the remainder of the tiip. The nar was traveling an average rate of
60
m
p
60 \mathrm{mp}
60
mp
trane
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Nora leans a
24
24
24
-foot ladder against a wall so that it forms an angle of
7
6
∘
76^\circ
7
6
∘
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
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A boat is heading towards a lighthouse, whose beacon-light is
135
135
135
feet above the water. The boat’s crew measures the angle of elevation to the beacon,
4
∘
4^\circ
4
∘
. 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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Makayla leans a
26
26
26
-foot ladder against a wall so that it forms an angle of
6
9
∘
69^\circ
6
9
∘
with the ground. What's the horizontal distance between the base of the ladder and the bottom of the wall? Round your answer to the nearest tenth of a foot if necessary.
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A bowling ball moving with a velocity of
3
V
3V
3
V
to the right collides elastically with a beach ball moving at a velocity
2
V
2V
2
V
to the left. The bowling ball barely slows down.What is the approximate velocity of the beach after the collision?
\newline
a.
V
V
V
\newline
b.
3
V
3V
3
V
\newline
c.
5
V
5V
5
V
\newline
d.
8
V
8V
8
V
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A boat is heading towards a lighthouse, whose beacon-light is
113
113
113
feet above the water. The boat’s crew measures the angle of elevation to the beacon,
1
5
∘
15^\circ
1
5
∘
. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.
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If you place a
32
32
32
-foot ladder against the top of a building and the bottom of the ladder is
24
24
24
feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.
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Amira leans a
16
16
16
-foot ladder against a wall so that it forms an angle of
6
6
∘
66^\circ
6
6
∘
with the ground. What's the horizontal distance between the base of the ladder and the bottom of the wall? Round your answer to the nearest hundredth of a foot if necessary.
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A monkey is swinging from a tree. On each swing, she travels along an arc that is
1
2
\frac{1}{2}
2
1
as long as the previous swing's arc. The total length of the arcs from her first
n
n
n
swings is
S
S
S
meters. How long was the monkey's
n
th
n^{\text{th}}
n
th
swing? Round your final answer to the nearest meter.
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A boat is heading towards a lighthouse, whose beacon-light is
113
113
113
feet above the water. The boat’s crew measures the angle of elevation to the beacon,
1
5
∘
15^\circ
1
5
∘
. What is the ship’s horizontal distance from the lighthouse (and the shore)?
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Elizabeth wants to use a sheet of fiberboard
27
27
27
inches long to create a skateboard ramp with a
1
7
∘
17^{\circ}
1
7
∘
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 if necessary.
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Question
\newline
A boat is heading towards a lighthouse, whose beacon-light is
148
148
148
feet above the water. The boat's crew measures the angle of elevation to the beacon,
8
∘
8^{\circ}
8
∘
. 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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Peggy the Pig built a house of sticks. The stick-house can withstand wind speeds up to
47
k
m
47 \mathrm{~km}
47
km
per hour.
\newline
Choose the best approximation of the highest wind speed that Peggy's stick-house can withstand.
\newline
Choose
1
1
1
answer:
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You are standing
42
42
42
feet away from the base of the Statue of Liberty looking up at an angle of
82.
2
∘
82.2^\circ
82.
2
∘
. How tall is the statue?
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2
2
2
. A motorboat took
5
5
5
hours to travel a distance of
60
60
60
k
m
\mathrm{km}
km
up a river, against the current. The return trip took
3
3
3
hours. Find the speed of the boat in still water and the speed of the current.
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A
35
35
35
foot ladder is set against the side of a house so that it reaches up
21
21
21
feet. If Elijah 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?
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One of the legs of a right triangle measures
1
cm
1\,\text{cm}
1
cm
and its hypotenuse measures
17
cm
17\,\text{cm}
17
cm
. Find the measure of the other leg. If necessary, round to the nearest tenth.
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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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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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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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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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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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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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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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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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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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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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