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Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
1.
What is the length of x?
19 cM
33 cm
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2.
y
Calculate the measure of angle e
-= 5) ,Jc
=
5
)
3.
"
Find each of the indicated sides.
6.3m
cAr s_2_t3
ojci
(0.
'ft
)C= Tt rv\
1
Cr_
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
4.
A piece of plywood is cut into the shape shown. Calculate the dimensions of the
plywood.
6 ft
5.
A woman is standing on one side of a deep ravine. The angle of depression to the
bottom of the far side of the ravine is 52° and the ravine is 120 m across. How deep
is the ravine? Draw a sketch.
2
Grade 11 Essential Math —Twenty Delightful Trigonometry Problems
6.
Justin wants to line the perimeter of his patio with a paving stone border. What is the
perimeter of his patio?
15m
20n1
\
t TT, b
3
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
7.
Pauline is building a fence around her vegetable garden, shown below. What length of
fence will she need to build?
5m
49.4
c1c)
1.75 m
2.75 m
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3
5 t 2,
s
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4
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75- 4-
9
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
8.
Jim is installing carpet in a den. Using the floorplan below, calculate the area of
carpet Jim will need to buy.
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to aS-e
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Bra
t-11 Al-eat
9.
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96 rfri
A tree casts a shadow that is 12.4 m long and the angle of elevation to the sun is 38°.
How tall is the tree?
12.4 m
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5
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
10.
During a plunge, a submarine travels a distance of 350 m while dropping 200 m.
What was its angle of depression, and how far did it travel horizontally? Draw a sketch.
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f
a,
2_.4 a
.sit 8 c c _
e,
11.
8 1, 2-
ug-15 "
Sasha is building a playhouse for his cousin. He has cut out this piece of plywood for the
back of the house. Calculate the indicated dimensions.
2_
s
=
4 ft
6
, S3
37
-41
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
12.
A flagpole is supported by two guy wires, each attached to a peg in the ground 4 m
from the base of the pole. The guy wires have angles of elevations of 35' and 45'.
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2- 8
a)
How much higher up the flagpole is the top guy wire attached?
yvv
b)
Jskut-c-
How long is each guy wire/
a
7
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
13.
From the top of a 200 m-tall office building, the angle of elevation to the top of another
building is 400. The angle of depression to the bottom of the second building is 25. How
tall is the second building?
9
B2
200 v"
?
B1
2_ 0
9. 5
221.51
-F-a,v14 3
if 2s
rp
17
3c;
0-00
8
9
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
14.
An extension ladder must be used at an angle of elevation of 65°. At its shortest length,
it is 18 feet long. Fully extended, it has a length of 32 feet. Draw a sketch.
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tc/
a.3 fox.
a)
How much higher up a building will it reach when it is fully extended, compared
to its shortest length?
(2,7
29,D — /4, S
b)
How much farther from the house must the base be when it is fully extended,
compared to its shortest length?
I8
Lp
3 7—
r7c 6
c—.
Grade 11 Essential Math —Twenty Delightful Trigonometry Problems
16.
Zach can see the top of a 180 m cell phone tower at an angle of elevation of 32', and
Norm can see it at an angle of elevation of 50'. How far apart are Zach and Norm if they
are on a straight line with the tower? There are two possibilities. Draw a sketch of both
possibilities and solve.
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18°
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4
3 ci vyk._
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
17.
A roller coaster has a track that drops at an angle of depression of 25° from a height
of 14.9 m. When it reaches the ground, in travels horizontally for 8 m. It then rises
at an angle of elevation of 47' to a height of 26.8 m.
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ILO
4-51,016v‘
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a)
7 ' 'I
What is the total horizontal distance covered by this portion of track?
52 /,
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--f&LK 9
b)
r
ill
What is the total distance travelled by ea car on this -portion of the roller
coaster track?
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11
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
18.
An airplane is flying 100 km north and 185 km west of an airport. It is flying at a
height of 7 km. Draw a sketch.
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a)
What is the straight-line distance to the airport?
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b)
°
3 le'vr\
What is the angle of elevation of the airplane, from the point of view of the
airport?
l
ot
Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
19.
Genevieve is standing on the top of a building that is 109 m tall. At an angle of elevation
of 41°, she views the top of the neighbouring building, which is 147m tall. Draw a sketch.
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14S
a)
How far apart are the buildings?
b)
If Genevieve looks down to the base of the neighbouring building, what is the
angle of depression?
to S
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13
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Grade 11 Essential Math — Twenty Delightful Trigonometry Problems
20.
Malcolm is on a canoe trip, travelling across a lake. He sees a tall tree on the shoreline in
the distance, and wants to estimate its height. He estimates that he is about 100 m from
the tree, and that the angle of elevation to the top of the tree is about 20'. Draw a
sketch.
( 06' wk
cccicj
Tn
a)
3 (0 • Li viN
1
What is the height of the tree?
3 (c) ,4 1/4n
b)
If Malcolm paddles closer to the tree and then views the top at an angle of
elevation of 36', how much closer to the tree will he have paddled?
S
14