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Angle of Elevation and Depression: Solving Word Problems

Learn how to find the angle of elevation and depression in various scenarios and solve word problems involving height, distance, and angles.

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Angle of Elevation and Depression: Solving Word Problems

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  1. Coordinates of P

  2. How did you do?Homework Solutions x = 9.0 x = 36.9º

  3. Answers to Page 472 5) 12.3 27) w+5,x=4.7 7) 2.5 9) 21.4 11) 32 13) 48 15) 63 21)44 and 136

  4. 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

  5. Find the angle between a horizontal line and another line. • 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.

  6. Example: Find the angle between the x-axis and y=3/4 x +2

  7. Try another one:The x axis and y=2x-5

  8. Up a notch:y=3y=4/5 x+3

  9. Angles ofElevationandDepressionToolkit #9.3 Today’s Goal(s): To use angles of elevation and depression to solve word problems.

  10. Understanding Angles of ElevationandDepression 38 38

  11. Angles of Elevation and Depression are CONGRUENT! Angle of Elevation • Looking UP! • INSIDE right triangle.

  12. Angles of Elevation and Depression are CONGRUENT! Angle of Depression • Looking DOWN! • OUTSIDE right triangle.

  13. Using the angle of depression!Remember, this angle is “depressed” and wants to get inside the triangle!

  14. 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?

  15. 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?

  16. 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?

  17. 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?

  18. 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!!

  19. 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.

  20. 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?

  21. 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?

  22. 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?

  23. 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.

  24. 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.

  25. 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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