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Name:______________________Date: ___________Chapter 8: Right Triangles & Trigonometry 4589145245110020000Section 8.4: Angles of Elevation & DepressionDO NOW1) Identify the pairs of alternate interior angles. 2) Use your calculator to find tan 30° to the nearest hundredth.3) Solve tan54°=2500x . Round to the nearest hundredth.5591175285750005343525351155020000Objectives of Lesson: TSW solve problems involving angles of elevation and angles of depression.Why learn this? Pilots and air traffic controllers use angles of depression to calculate distances.Example 1: Classifying Angles of Elevation and DepressionClassify each angle as an angle of elevation or an angle of depression.4341495508040000200001 Example 2: Classifying Angles of Elevation and DepressionClassify each angle as an angle of elevation or an angle of depression.4 4000500298450020000Example 3: Use the diagram above to classify each angle as an angle of elevation or angle of depression.a. 5b. 6Example 4: Finding Distance by Using Angle of ElevationThe Seattle Space Needle casts a 67-meter shadow. If the angle of elevation from the tip of the shadow to the top of the Space Needle is 70?, how tall is the Space Needle? Round to the nearest meter.Draw a sketch to represent the given information. Let A represent the tip of the shadow, and let B represent the top of the Space Needle. Let y be the height of the Space Needle. Example 5: An air traffic controller at an airport sights a plane at an angle of elevation of 41°. The pilot reports that the plane’s altitude is 4000 ft. What is the horizontal distance between the plane and the airport? Round to the nearest footExample 5.5: What if…? Suppose the plane is at an altitude of 3500 ft and the angle of elevation from the airport to the plane is 29°. What is the horizontal distance between the plane and the airport? Round to the nearest foot.Example 6: Finding Distance by Using Angle of DepressionAn ice climber stands at the edge of a crevasse that is 115 ft wide. The angle of depression from the edge where she stands to the bottom of the opposite side is 52?. How deep is the crevasse at this point? Round to the nearest foot. Draw a sketch to represent the given information. Let C represent the ice climber and let B represent the bottom of the opposite side of the crevasse. Let y be the depth of the crevasse. 4733925415290020000Example 7: A forest ranger in a 90-foot observation tower sees a fire. The angle of depression to the fire is 7°. What is the horizontal distance between the tower and the fire? Round to the nearest foot.Draw a sketch to represent the given information. Let T represent the top of the tower and let F represent the fire. Let x be the horizontal distance between the tower and the fire.Example 7.5: What if…? Suppose the ranger sees another fire and the angle of depression to the fire is 3°. What is the horizontal distance to this fire? Round to the nearest foot.Example 8: Shipping ApplicationAn observer in a lighthouse is 69 ft above the water. He sights two boats in the water directly in front of him. The angle of depression to the nearest boat is 48?. The angle of depression to the other boat is 22?. What is the distance between the two boats? Round to the nearest foot. Step 1 Draw a sketch. Let L represent the observer in the lighthouse and let A and B represent the two boats. Let x be the distance between the two boatsStep 2 Find y. Step 3 Find z.Step 4 Find x.Example 9 A pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is 78°, and the angle of depression to the second airport is 19°. What is the distance between the two airports? Round to the nearest foot.Step 1 Draw a sketch. Let P represent the pilot and let A and B represent the two airports. Let x be the distance between the two airports.Step 2 Find y. Step 3 Find z.Step 4 Find x.smilardo. - homework: worksheets: link to book and more ................
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