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Angles of Elevation and Depression

Angles of Elevation and Depression. Ship and Lighthouse. The angle of elevation from a ship to the top of a 42 meter tall lighthouse on the shore measures 33 degrees. How far is the ship from the lighthouse? (assume the horizontal line of sight meets the bottom of the lighthouse) .

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Angles of Elevation and Depression

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  1. Angles of Elevation and Depression

  2. Ship and Lighthouse • The angle of elevation from a ship to the top of a 42 meter tall lighthouse on the shore measures 33 degrees. How far is the ship from the lighthouse? (assume the horizontal line of sight meets the bottom of the lighthouse)

  3. Airplane Landing • A pilot is preparing to land a jet on an approach path that forms a 20 degree angle with the aircraft carrier. The plane is currently at an altitude of 10000 feet. How long is the approach path (hypotenuse)?

  4. Landscaping • You are planting trees as part of your new landscaping job. In order to determine the proper length of a guy wire (this is the wire that holds the tree straight up) you know that each wire is attached at a height of 5 feet up the tree and makes a 65 degree angle with the ground. How long should the guy wires be from the tree to the ground?

  5. Wreckage • A salvage ship’s sonar locates wreckage at a 12 degree angle of depression. A diver is lowered 40 meters to the ocean floor. How far does the diver need to walk along the ocean floor to get to the wreckage?

  6. Vector Trig While floating down a river with a 2.75 mph current, Alicia decides to swim directly toward the river bank. She can swim at 0.75 mph in still water. What is the actual speed at which she moves toward the bank? (This is a vector physics type problem) At what angle will she swim towards the bank?

  7. Fire Tower Problem • Two fire watchtowers 8.4 km apart spot a fire at the same time. Tower Whomping Willow reports the fire at a 36 degree angle measure from its line of sight to Treebeard Tower. Treebeard Tower reports a 68 degree angle measure between the fire and Tower Whomping Willow. How far is the fire from each tower?

  8. Fire Tower Problem Picture FIRE d1 d2 h 8.4km

  9. Trig Hints • Hints • set up the base as x and 8.4-x • Find both parts in terms of h • Set them equal to each other • Solve for x • Use x and cosines to find each hyp

  10. Practice • John flies a kite in his yard. The angle between the ground and the kite is 21 degrees. If John lets out 30 yards of string, how high is the kite above the ground?

  11. #23 Correction • Mr. D is planning on cutting down a dead tree in his yard. He does not want the tree to hit his house, he measures to find that the tree is 58 feet away from the house; and the only way to cut it down is towards his own house to avoid all of the neighbor’s houses. Mr. D measures the angle between a point on the ground 40 feet away and the top of the tree and finds that it is 37 degrees (the point on the ground is 40 feet away from the bottom of the tree). How tall is the tree? When the tree falls will it hit his own house?

  12. Warm Up: • 1) Turn in your warm ups: PLEASE WRITE YOUR NAME ON THEM! • 2) Turn in your Ch. 5 Review Packets • 3) Turn in your Ch. 5 Perf Task for the early Bonus (Perf Task is due Nov 1) • 4) Prepare for Test – clear off desks, get out calculator etc.

  13. Warm Up: • 1) Find the vertex for the below: • 2) Find the y-intercept, Domain and Range

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