Download Similarity Trigonometry Student Module

Similarity/Trigonometry Student Module
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Similarity
1.
Δ ABC is similar to Δ DEF. Find the missing angles.
B
a.
E
24˚
D
88˚
F
88˚
C
A
B
E
b.
50˚
A
2.
a.
32˚
D
C
Δ ABC is similar to Δ DEF. Find the missing sides.
A
7
E
F
9
10
D
C
B
42
B
F
b.
21
D
3
4
E
A
35
C
F
B
c.
E
20
100
D
A
3.
120
24
F
C
Δ ABC is similar to Δ DEF.
a.
b.
c.
d.
e.
f.
Find EF.
Find ED.
Find the perimeter of Δ ABC.
Find the perimeter of Δ DEF.
What is the ratio of the perimeter of Δ ABC to the perimeter of
Δ DEF?
What is the ratio of the perimeter of Δ DEF to the perimeter of
Δ ABC?
4.
Angles C and F are right angles.
a.
b.
c.
d.
e.
5.
What information would be needed to prove that Δ ABC is similar to
Δ DEF?
Find the area of Δ ABC.
Find the area of Δ DEF.
What is the ratio of the area of Δ ABC to the area of Δ DEF?
What is the ratio of the perimeter of Δ ABC to the perimeter of
Δ DEF?
Δ GHI is similar to Δ JKL.
a.
b.
If the perimeter of Δ JKL is p, what is the perimeter of Δ GHI?
If the area of Δ JKL is a, what is the area of Δ GHI?
Round the answers to the nearest tenth in the following problems.
6.
An art student wants to enlarge a triangle with the sides 8, 8, and 10 cm.
The new triangle will have a measurement of 15 cm on its longest side. How long
will the other sides be on the new triangle?
7.
A flagpole casts a shadow 24 feet long. A 6-foot man standing nearby casts
a shadow of 8 feet. How tall is the flagpole?
8.
A 9-foot ladder leans against a building 7 feet above the ground. If a 15foot ladder was propped up against the building at the same angle with the ground,
how far would it reach up the building?
9.
A 6-foot ladder leans against a building. The foot of the ladder is 2 feet
away from the building. If a 9-foot ladder is propped against the building at the
same angle with the ground, the foot of the new ladder would be how far away
from the building?
Trigonometry
Use ΔABC to find the following measures. Round to tenths.
C
A
10.
11.
12.
13.
14.
15.
If m<B = 30° and BC = 12, find AC.
If m<B = 49° and BC = 92, find AB.
If m<B = 50° and AC = 10, find BC.
If m<B = 48° and AC = 18, find AB.
If AB = 6 and BC = 23, find m<B.
If AC = 34 and BC = 72, find m<B.
B
Round the answers to the nearest tenth in the following problems.
16.
A loading ramp is 30 feet long and forms an angle measuring 12° with the
ground. How high is the top end of the ramp off the ground?
17.
A flagpole is 50 feet tall and casts a shadow of 62 feet. Find the angle of
elevation with the sun.
18.
A man on a cliff looks out across the water at an approaching sailboat. If
the man is 400 feet high and the angle of depression is 58°, what is the line of
sight distance of the sailboat from the man?
19.
A wrecking company must knock down an old building. In order to determine
where it will fall, it is necessary to find its height. The top of the building is
viewed from a point 150 meters from its base. The angle of elevation is 33°. Find
the height of the building.
20.
The Eiffel Tower in Paris casts a shadow of 160 meters when the angle of
elevation with the sun is 57°. What is the height of the Eiffel Tower?
21.
A forest ranger in a tower spotted a fire. The angle of depression from the
ranger to the fire was 3°. The tower is 30 meters high. What is the distance
from the base of the tower to the fire?
22.
A roller coaster track starts at the top of a hill and carries riders to the
ground. The track forms an angle of 60° with the level ground at the bottom of
the hill. The hill has an altitude of 100 feet. How long would the track need to be?
23.
Part of a road that is 450 meters in length has a slight incline. The vertical
rise is 10 meters. Find the angle of elevation.
24.
A banister for a set of stairs is 8 feet in length. The vertical rise is 1 foot.
What is the measure of the angle of depression for the banister?
25.
Vu, a bystander at the Pegasus Parade, is lying on his back and observing a
large balloon of a cartoon character, floating directly above Broadway Street. Vu
is located 30 feet from a point on the street directly beneath the balloon. To see
the top of the balloon, he looks up at an angle of 58. To see the bottom of the
balloon, he looks up at an angle of 47.
a.
To the nearest tenth, what is the distance, in feet, from the top of
the balloon to the street?
b.
To the nearest tenth, what is the distance, in feet, from the bottom
of the balloon to the street?
c.
To the nearest tenth, how tall, in feet, is the balloon?
Similarity
26.
If two polygons are similar, then what must be true about the corresponding
angles?
a.
b.
c.
d.
They are complementary.
They are congruent.
They are linear pairs.
They are supplementary.
27.
If two polygons are similar, then what must be true about the corresponding
sides?
a.
They are congruent.
b.
They are parallel.
c.
They are proportional.
d.
They are similar.
28.
Which of the following would be sufficient to show that two triangles are
similar?
a.
Two sides of one are proportional to two sides of the other.
b.
A side of one is congruent to a side of the other.
c.
Two angles of one are congruent to two angles of the other.
d.
An angle of one is congruent to an angle of the other.
29.
Moody wants to find the height of the tallest building in his city. He stands
144 feet away from the building. There is a tree 32 feet in front of him, which he
knows is 25 feet tall. How tall is the building?
a.
b.
c.
d.
87.5 feet
112.5 feet
143.36 feet
184.32 feet
Trigonometry
30.
A slide 3.8 meters long makes an angle of 28  with the ground. How high is
the top of the slide above the ground? Round to hundredths.
a.
b.
c.
d.
1.78 meters
1.86 meters
2.02 meters
3.36 meters
31.
Find the cos (B).
B
25
24
A
a.
b.
c.
d.
24
25
7
24
7
25
24
7
7
C