Download 10.1: The Tangent Ratio

10.1: The Tangent Ratio
0011 0010 1010 1101 0001 0100 1011
Expectation:
G1.3.1: Define the sine, cosine, and tangent
of acuteangles in a right triangle as ratios
of sides. Solve problems about angles,
side lengths, or areas using trigonometric
ratios in right triangles.
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10.1: The Tangent Ratio
0011 0010 1010 1101 0001 0100 1011
The length of arc XY of a circle is equal to ⅙
of the circumference of the circle. The
length of the arc is 7π inches? What is the
radius, in inches, of the circle?
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10.1: The Tangent Ratio
Tangent
0011 0010 1010 1101 0001 0100 1011
a. Draw Δ ABC w/ m A=40, m  B = 90
and AB=2
b. Draw Δ DEF w/ m  D=40, m  E = 90
and DE=2.5
c. Draw Δ GHI w/ m  G=40, m  H = 90
and GH=3
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10.1: The Tangent Ratio
Tangent
0011 0010 1010 1101 0001 0100 1011
d. Determine BC, EF and HI
e. Compare
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BC EF HI
,
,
AB DE GH
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10.1: The Tangent Ratio
Tangent Ratio
0011 0010 1010 1101 0001 0100 1011
Defn: In a right triangle with acute angle,
 A, with a measure of θ (theta), the
tangent of A (tan A = tan A = tan θ) is
the ratio of the length of the leg opposite
A to the length of the leg adjacent to
A.
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10.1: The Tangent Ratio
opposite
Tan θ =
adjacent
opposite
0011 0010 1010 1101 0001 0100 1011
1
θ
adjacent
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10.1: The Tangent Ratio
opposite
Tan α =
adjacent
adjacent
0011 0010 1010 1101 0001 0100 1011
α
1
opposite
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10.1: The Tangent Ratio
Give the tangent of A and B
for the triangle below.
0011 0010 1010 1101 0001 0100 1011
A
13
5
B
12
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10.1: The Tangent Ratio
Using a Trig Table (page 870)
0011 0010 1010 1101 0001 0100 1011
What is tan θ if:
a. θ = 30
b. θ = 75
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10.1: The Tangent Ratio
Arc Tangent
0011 0010 1010 1101 0001 0100 1011
The arc tangent tells us the measure of the
angle with the given tangent ratio.
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10.1: The Tangent Ratio
Arc Tangent
0011 0010 1010 1101 0001 0100 1011
What is θ if:
a. tan θ = 1.483
b. tan θ = .176
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10.1: The Tangent Ratio
Tangent on a Calculator
0011 0010 1010 1101 0001 0100 1011
TAN
-1
TAN
tangent θ
arc tangent θ
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Calculator must be set in
degree mode!!!!!!
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10.1: The Tangent Ratio
Using your calculator, what is:
0011 0010 1010 1101 0001 0100 1011
tan 23?
tan 45?
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10.1: The Tangent Ratio
What is the measure of an angle
whose tangent ratio is:
0011 0010 1010 1101 0001 0100 1011
.6532
.0175
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10.1: The Tangent Ratio
Calculate the measure of A to the nearest
tenth of a degree.
0011 0010 1010 1101 0001 0100 1011
B
5
A
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12
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C
10.1: The Tangent Ratio
Calculate BC below to the nearest
hundredth.
0011 0010 1010 1101 0001 0100 1011
B
C
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34°
15
A
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10.1: The Tangent Ratio
Calculate AC below to the nearest
hundredth.
0011 0010 1010 1101 0001 0100 1011
B
10
A
18°
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C
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10.1: The Tangent Ratio
The directions for assembling a pool ladder state that the
ladder should be placed at an angle of 75 relative to level
ground. If the pool walls are 6 feet tall, which of the
0011 0010following
1010 1101expressions
0001 0100 1011
gives the distance in feet, that the
ladder should be placed away from the bottom edge of the
pool to comply with the directions?
A.
B.
C.
D.
E.
6
tan 75
tan 75
6
1
6 tan 75
6 tan 75
tan (6 75°)
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10.1: The Tangent Ratio
Ice Cream Anyone?
0011 0010 1010 1101 0001 0100 1011
Ben and Jerry are on one side of river and Edy
is on the other.
Ben is 20 meters directly south of Jerry.
Jerry and Edy are directly across the river
from each other.
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10.1: The Tangent Ratio
Ice Cream Anyone?
0011 0010 1010 1101 0001 0100 1011
If Ben points at Edy and Jerry at the same
time, his arms form a 54° angle.
How far is it across the river? Round your
answer to the nearest tenth of a meter.
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10.1: The Tangent Ratio
J
E
0011 0010 1010 1101 0001 0100 1011
20
54°
B
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10.1: The Tangent Ratio
0011 0010 1010 1101 0001 0100 1011
As shown in the figure below, what is the
tangent of angle C?
B
5
1
A
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C
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10.1: The Tangent Ratio
Assignment
0011 0010 1010 1101 0001 0100 1011
pages 635-637,
# 13-33 (odds), 35-39 (all)
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10.1: The Tangent Ratio