How to make the measurements: Trigonometric relations: cos(A) = d/z sin(A) = f/z tan(A) = f/d = /x В A h d. An object a distance, d, away having a full height, h. f is the height relative to eye level and g is the eye level height of the observer. A stick with a length, I, held a distance, x, away from eye level. The bottom of the stick is angle, A, can easily be held at eye level and the top of the stick overlaps with the top of the object regarding the observer's line of sight. Since l/x = f/d due to the similar triangles formed, the determined as well as the height of the object, f, relative to eye level, g. The full height of the object is then, h = f+g 1. What is the formula to compute the angle “A", using the object distance and its height relative to eye level? 2. What is the formula to compute the angle “A", using stick length and the distance it is held from your eye? away 3. What is the formula to compute the height of the of the object relative to eye level "f', using the object distance, stick length and the distance away that the stick is held? 4. What is the formula for the full height of the object "h", using the object distance, stick length, distance away that the stick is held, and observer's eye level height?
How to make the measurements: Trigonometric relations: cos(A) = d/z sin(A) = f/z tan(A) = f/d = /x В A h d. An object a distance, d, away having a full height, h. f is the height relative to eye level and g is the eye level height of the observer. A stick with a length, I, held a distance, x, away from eye level. The bottom of the stick is angle, A, can easily be held at eye level and the top of the stick overlaps with the top of the object regarding the observer's line of sight. Since l/x = f/d due to the similar triangles formed, the determined as well as the height of the object, f, relative to eye level, g. The full height of the object is then, h = f+g 1. What is the formula to compute the angle “A", using the object distance and its height relative to eye level? 2. What is the formula to compute the angle “A", using stick length and the distance it is held from your eye? away 3. What is the formula to compute the height of the of the object relative to eye level "f', using the object distance, stick length and the distance away that the stick is held? 4. What is the formula for the full height of the object "h", using the object distance, stick length, distance away that the stick is held, and observer's eye level height?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Analytic Trigonometry
Section2.1: Using Fundamental Identities
Problem 67E
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Transcribed Image Text:Table 2: Length Units
Millimeters | Centimeters
Meters
Kilometers
Inches
Feet
Yards
Miles
km
yd
0.003281 | 0.001094 6.21e-07
0.393701 0.032808 0.010936| 0.000006
3.28084 | 1.093613 | 0.000621
39370.08 3280.84 | 1093.613 0.621371
0.083333 0.027778 0.000016
mm
cm
m
in
ft
mi
0.001
0.01
1
0.1
0.000001
0.03937
10
1
0.00001
1000
1000000
25.4
304.8
914.4
100
100000
0.001
1
0.000025
0.000305
0.000914
39.37008
2.54
30.48
91.44
1000
0.0254
0.3048
0.9144
1
12
36
1
3
0.333333 0.000189
0.000568
1
1609344
160934.4
1609.344
1.609344
63360
5280
1760
1
Transcribed Image Text:How to make the measurements:
Trigonometric relations:
cos(A) = d/z
sin(A) = f/z
tan(A) = f/d = 1/x
В
f
h
A
A
d
A stick with a length, 1, held a
distance, x, away from eye
An object a distance, d, away
having a full height, h. f is the
height relative to eye level and g
is the eye level height of the
observer.
Since 1/x = f/d due to the
similar triangles formed, the
angle, A, can easily be
determined as well as the
level. The bottom of the stick is
held at eye level and the top of
the stick overlaps with the top
of the object regarding the
observer's line of sight.
height of the object, f, relative
to eye level, g. The full height
of the object is then, h = f+g
1.
What is the formula to compute the angle "A", using the object distance and its height relative to
eye level?
2. What is the formula to compute the angle “A", using stick length and the distance it is held away
from your eye?
3. What is the formula to compute the height of the of the object relative to eye level “f", using the
object distance, stick length and the distance away that the stick is held?
4. What is the formula for the full height of the object "h", using the object distance, stick length,
distance away that the stick is held, and observer's eye level height?
5. Now you will proceed to determine some object heights given a scenario. Fill in the tables
regarding each scenario.
N
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