Angles of Elevation and Depression.ppt

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Angles of Elevation and Depression.ppt Powered By Docstoc
					          Warm Up

                8
                            5




Solve the triangle above.
 Angles of Elevation and
      Depression

- Applications of our trig functions!
              Application #1
A 35 foot ladder is leaned up against the side of a
  house at a 65ْ angle with the ground. Find the
  distance from the base of the house to the foot
  of the ladder and the height reached by the
  ladder.
Surveyors
#2:
A surveyor sighted from the bank of a river directly
across it to a tree on the opposite bank. He then
turned exactly 90° to the right, and paced off 200
feet. He then sighted the same tree with an angle
of 20°. How wide is the river?




                            r = 72.79 ft
              Vocabulary
• Angle of elevation




• Angle of depression
 Drawing and accurately labeling a diagram is essential in
 problem solving!!!!!!


1. From a point on the ground 150 meters from the base of a
   cliff, the angle of elevation to the top is 27 degrees. How
   high is the cliff?
2. An airplane climbed 1250 feet while making 3 miles of
   airline distance (horizontal distance). Find the angle at
   which the airplane climbed. Note: 1 mile = 5280 feet
3. From a lighthouse which stands 40 meters above the level
   of a lake, the angle of depression of a buoy on the water is
   18 degrees. Find the distance of the buoy from the base
   of the lighthouse.
Now a bit harder:

4. From the window of an office building, the angle of elevation of the top of the
   Empire State Building is 57 degrees and the angle of depression of a point on
   the ground directly below the top of the skyscraper is 13 degrees. The buildings
   are known to be 167 feet apart. How high is the Empire State Building?




                                                       57
                                                       13




                                             Not to scale......at all.
                  Two Step Problems
                                                      CN tower in Toronto Canada
• The angle of elevation to the top of the building is
  43° and the angle of elevation to the top of the
  antenna is 61°. If the glass floor is 342 m tall, what
  is the height of the “sky pod”?
                      Warm Up
• Two office buildings are 29 ft apart. The height of the
  taller building is 609 ft. The angle of depression from the
  top of the taller building to the top of the shorter building
  is 15°. Find the height of the shorter building.
5. A vertical tree stands on a slope that is inclined at an angle of 12 degrees
   with the horizontal. When the angle of the sun measures 30 degree, the
   shadow of the tree down the slope is 18 meters long. How tall is the tree?
Challenge: From the top of a 30 meter high lighthouse, the keeper measures
the angles of depression to two boats, one directly west of the lighthouse and the
Second due south. The angles of depression are found to be 8 and 14 degrees,
Respectively. How far are the two boats apart? (to the nearest tenth)
• A meteorologist measures the angle of
  elevation of a weather balloon as 41°. A
  radio signal from the balloon indicates that
  it is 1503 m from her location. How high is
  the weather balloon above the ground?
• The world’s tallest unsupported flagpole is
  282 ft tall in Surrey, British Colombia. The
  shortest shadow cast by the pole during
  the year is 137 ft long. What is the angle
  of elevation of the sun when the shortest
  shadow is cast?

				
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