Download Right Triangles 5 Activity Key

Right Triangles 5
Angles of Elevation & Depression
Name ___________________________
Activity
1. a) You are standing on the ground at the Plano Balloon Festival.
Which way do you have to look to see the balloons that are in flight?
b) You are the pilot of one of the hot air balloons.
Which way do you have to look to see a person on the ground?
c)
A person in an airplane at a height of 500 m sees a grain silo on the ground.
Which way does the person have to look to see the silo?
d) A tourist in New York City looks at the top of the Empire State Building.
Which way does the person have to look to see the top?
e) A bird watcher on the ground spots a robin in a tree.
Which way does the bird watcher have to look to see the bird?
2. In trigonometry, we use two different types of angles, angles of elevation and angles of depression.
a) Which of the questions in problem #1 do you think represent angles of elevation?
Why?
b) Which of the questions in problem #1 do you think represent angles of depression?
Why?
3.
Ralph is standing on the
deck of his sailboat when he
notices a helicopter directly
overhead and a lighthouse
on top of the cliff.
a) Draw in horizontal lines from Ralph to the shore and from the helicopter to the
lighthouse. What relationship do these two lines have?
b) Draw a line to represent Ralph’s line of sight to the lighthouse. Label the angle formed by
this line and the horizontal line to the shore as 1. Label the angle formed by this line
and the line between the lighthouse and the helicopter as 2.
What relationship do these two angles have? Why?
c) In both angles, there must be a ____________________ line as one of the sides.
(horizontal or vertical)
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Right Triangles 5
4. A person standing on a cliff looks up to see a hot air balloon and
then looks down to see a sailboat.
a) Which angle is the angle of elevation?
b) Which angle is the angle of depression?
Person
Hot Air
Balloon
1
2
Sailboat
Label the triangle provided for each problem and then answer each question
5. An observer in an airplane at a height of 500 m sees a car at an angle of
depression of 31°. If the plane is over a barn, how far is the car from the
barn?
6. The angle of elevation from point A to the top of a cliff is 38°. If point A
is 80 feet from the base of the cliff, how high is the cliff?
A
7. The string of a kite makes a 50° angle with the ground. The kite string
is 40 feet long. How high above the ground is the kite if the hand of the
person holding the kite is 6 feet above the ground?
8. The Observation Deck of John Hancock Center is on the 94th floor,
which is 1030 feet above the ground. The Skydeck of the
Sears Tower is on the 103rd floor, which is 1335 feet from the ground.
The John Hancock Center is 1.7 miles or 8976 feet from the Sears Tower.
If Hanna is on the observation deck of the Hancock Center and Arnoldo
is on the Skydeck of the Sears Tower, What is the angle of elevation
from Hanna to Arnoldo?
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Right Triangles 5
Right Triangles 5 Activity Key
Angles of Elevation & Depression
Name ___________________________
1. a) You are standing on the ground at the Plano Balloon Festival.
up
Which way do you have to look to see the balloons that are in flight?
b) You are the pilot of one of the hot air balloons. down
Which way do you have to look to see a person on the ground?
c)
A person in an airplane at a height of 500 m sees a grain silo on the ground.
Which way does the person have to look to see the silo?
down
d) A tourist in New York City looks at the top of the Empire State Building. up
Which way does the person have to look to see the top?
e) A bird watcher on the ground spots a robin in a tree. up
Which way does the bird watcher have to look to see the bird?
2. In trigonometry, we use two different types of angles, angles of elevation and angles of depression.
a) Which of the questions in problem #1 do you think represent angles of elevation?
Why? a, d, e
b) Which of the questions in problem #1 do you think represent angles of depression?
Why? b, c
3.
2
Ralph is standing on the
deck of his sailboat when he
notices a helicopter directly
overhead and a lighthouse
on top of the cliff.
1
a) Draw in horizontal lines from Ralph to the shore and from the helicopter to the
lighthouse. What relationship do these two lines have? parallel
b) Draw a line to represent Ralph’s line of sight to the lighthouse. Label the angle formed by
this line and the horizontal line to the shore as 1. Label the angle formed by this line
and the line between the lighthouse and the helicopter as 2.
What relationship do these two angles have? Why? ll →  AI ’s
c) In both angles, there must be a __horizontal ___________ line as one of the sides.
(horizontal or vertical)
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Right Triangles 5
4. A person standing on a cliff looks up to see a hot air balloon and
then looks down to see a sailboat.
a) Which angle is the angle of elevation? 1
b) Which angle is the angle of depression? 2
Person
Hot Air
Balloon
1
2
Sailboat
Label the triangle provided for each problem and then answer each question
5. An observer in an airplane at a height of 500 m sees a car at an angle of
depression of 31°. If the plane is over a barn, how far is the car from the
barn?
832.1 m
6. The angle of elevation from point A to the top of a cliff is 38°. If point A
is 80 feet from the base of the cliff, how high is the cliff?
62.5 ft
A
7. The string of a kite makes a 50° angle with the ground. The kite string
is 40 feet long. How high above the ground is the kite if the hand of the
person holding the kite is 6 feet above the ground?
30.64 ft
8. The Observation Deck of John Hancock Center is on the 94th floor,
which is 1030 feet above the ground. The Skydeck of the
Sears Tower is on the 103rd floor, which is 1335 feet from the ground.
The John Hancock Center is 1.7 miles or 8976 feet from the Sears Tower.
If Hanna is on the observation deck of the Hancock Center and Arnoldo
is on the Skydeck of the Sears Tower, What is the angle of elevation
from Hanna to Arnoldo?
18.80 feet
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