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10.1: The Tangent Ratio. 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. - PowerPoint PPT Presentation
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10.1: The Tangent Ratio
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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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?
04/20/23 10.1: The Tangent Ratio
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Tangent
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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Tangent
d. Determine BC, EF and HI
e. CompareGH
HI ,
DE
EF ,
AB
BC
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Tangent Ratio
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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θop
po
site
adjacent
Tan θ =oppositeadjacent
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α
adja
cen
t
opposite
Tan α =oppositeadjacent
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5A 13
12B
Give the tangent of A and B for the triangle below.
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Using a Trig Table (page 870)
What is tan θ if:
a. θ = 30
b. θ = 75
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Arc Tangent
The arc tangent tells us the measure of the angle with the given tangent ratio.
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Arc Tangent
What is θ if:
a. tan θ = 1.483
b. tan θ = .176
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Tangent on a Calculator
TAN
TAN-1
tangent θ
arc tangent θ
Calculator must be set in degree mode!!!!!!
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Using your calculator, what is:
tan 23?
tan 45?
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What is the measure of an angle whose tangent ratio is:
.6532
.0175
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Calculate the measure of A to the nearest tenth of a degree.
A 12
5
C
B
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Calculate BC below to the nearest hundredth.
B
C A34°15
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Calculate AC below to the nearest hundredth.
AC
B
18°
10
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The directions for assembling a pool ladder state that the ladder should be placed at an angle of 75 relative to level ground. Which of the following expressions 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. 6 tan 75
E. tan (6 75°)
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6
tan 75
tan 75
6
1
6 tan 75
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Ice Cream Anyone?
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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Ice Cream Anyone?
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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J
B
E
54°
20
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As shown in the figure below, what is the tangent of angle C?
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A
1
B
C
5
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pages 635-637,
# 13-33 (odds), 35-39 (all)
Assignment
