Transcript Angles of Elevation and Depression Toolkit #9.3

Coordinates of P
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Homework Solutions
x = 36.9º
x = 9.0
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Answers to Page 472
5) 12.3
7) 2.5
9) 21.4
11) 32
13) 48
15) 63
21)44 and 136
27) w+5,x=4.7
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Answers to Page 479
5) 8.3
7) 17.0
9) 106.5
11) 21
13) 46
15) 24
23) w=37, x=7.5
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Find the angle between a
horizontal line and another
line.
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Graph it on graph paper.
Draw a right triangle.
Find the horizontal and vertical sides by
counting the blocks or using the
distance formula.
Write an equation using the tangent
function. Solve with the inverse
tangent button.
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Example: Find the angle between
the x-axis and y=3/4 x +2
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Try another one:
The x axis and y=2x-5
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Up a notch:
y=3
y=4/5 x+3
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Angles of
Elevation and Depression
Toolkit #9.3
Today’s Goal(s):
1.
To use angles of elevation and
depression to solve word problems.
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Understanding Angles of
Elevation and Depression
38
38
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Angles of Elevation and
Depression are CONGRUENT!
Angle of Elevation
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Looking UP!
INSIDE right triangle.
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Angles of Elevation and
Depression are CONGRUENT!
Angle of Depression
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Looking DOWN!
OUTSIDE right triangle.
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Using the angle of depression!
Remember, this angle is “depressed”
and wants to get inside the triangle!
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Example:
A man stands 12 ft. from the base of a tree. The
angle of elevation from his feet to the top of the
tree is 76. How tall is the tree?
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1.
a.
b.
A highway makes an angle 6 with the
horizontal. This angle is maintained for a
horizontal distance of 8 miles.
Draw and label a diagram to represent this situation.
To the nearest hundredth of a mile, how high does the highway
rise in this 8-mile section?
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2.
a.
b.
A forest ranger spots a fire from a 21-foot
tower. The angle of depression from
the tower to the fire is 12.
Draw a diagram to represent this situation.
To the nearest foot, how far is the fire from the base of the tower?
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3.
To approach the runway, a small plane must begin a
9 descent starting from a height of 1125 feet above
the ground. Draw and label the diagram and then to
the nearest tenth of a mile, how many miles from the
runway is the airplane at the start of this approach?
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4.
Divers looking for a sunken ship have defined the
search area as a triangle with adjacent sides of length
2.75 miles and 1.32 miles. The angle between the
sides of the triangle is 35. To the nearest hundredth,
find the search area.
Sneak Preview for lesson 9.5! 
You will need a new AREA formula for
this problem!!
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5.
Find the angle of elevation of the sun from the ground
to the top of a tree when a tree that is 10 yards tall
casts a shadow 14 yards long. Round to the nearest
degree.
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6.
A spotlight is mounted on a wall 7.4 feet above a
security desk in an office building. It is used to light an
entrance door 9.3 feet from the desk. To the nearest
degree, what is the angle of depression from the
spotlight to the entrance door?
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7.
To find the height of a pole, a surveyor moves 140 feet
away from the base o the pole and then, with a transit
4 feet tall, measures the angle of elevation to the top
of the pole to be 44. To the nearest foot, what is the
height of the pole?
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8.
A slide 4.1 meters long makes an angle of 35 with the
ground. Draw and label the diagram then to the
nearest tenth of a meter, how far above the ground is
the top of the slide?
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9.
The students in Ms. Crane’s class used a surveyor’s
measuring device to find the angle to be 72 from their
location to the top of a building. They also measured
their distance from the bottom of the building as 100 feet.
Draw the diagram to illustrate this information. Label x
for the height of the building. Solve.
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10.
A large totem pole in the state of Washington is 100
feet tall. At a particular time of day, the totem pole
casts a 249-foot-long shadow. Draw and label a
diagram to illustrate this information and find the angle
of elevation from the ground to the top of the pole.
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11.
a.
b.
c.
d.
From the top of a 210-foot lighthouse located at sea
level, a boat is spotted at an angle of depression of 23.
Draw a sketch to represent the situation.
Use the angle of depression to find the distance from the base of
the lighthouse to the boat.
Use another angle to verify the distance you found in part (b).
Use the Pythagorean Theorem to find the shortest distance from the
top of the lighthouse to the boat.
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