3. Angles of Elevation and Depression Sec: 8.4 Sol: G.8

4. Sometimes drawing a diagram of the situation described in a problem can help you to solve problems involving angles of elevation and depression. Angles of elevation or depression to two different objects can be used to find the distance between those objects.

5. Angles of Elevation and Depression The following is a pictorial example of angles of elevation and depression: This is the angle of elevation This is the angle of depression

6. Arbitrary line from the point of depression If an arbitrary line is drawn from the point of depression, we can assume that the line is parallel to the ground. If it is parallel to the ground, then the angle of depression is ________________ to the angle of elevation. x  x  arbitrary line from the point of depression

7. Example: Name the angles of elevation and depression in each figure:  of elevation: _______  of depression: _______  of elevation: _______  of depression: _______  of elevation: _______  of depression: _______  of elevation: _______  of depression: _______

8. Examples: You can use Trigonometric ratios to find the angles of elevation and depression. 1. Hanna is on the Observation Deck of the John Hancock Center on the 94 th floor, which is 1030 feet above the ground. Arnold is on the Skydeck of the Sears Tower on the 103 rd floor, which is 1335 feet from the ground. The John Hancock Center is 1.7 miles or 8976 feet from the Sears Tower. To the nearest tenth, what is the angle of elevation from Hanna to Arnold?

9. 2. A surveyor is 130 feet from a tower. The tower is 86 feet high. The surveyor’s instrument is 4.75 feet above the ground. Find the angle of elevation, to the nearest degree. 3. A ski slope is 550 yards long with a vertical drop of 130 yards. To the nearest tenth of a degree, find the angle of depression of the slope.

10. 4. Jordan is 50 feet from the tallest totem pole. The tallest totem pole, located in Canada, is 173 feet high. If Jordan’s eyes are 5 feet from the ground, find the angle (to the nearest tenth) of elevation for her line of sight to the top of the totem pole. 5. Dustin is visiting the Blue Ridge Parkway outside Floyd, Virginia. The angle of elevation for his line of sight to the top of the Blue Ridge Parkway Welcome Sign is 75 . If his line of sight is 6 feet from the ground and the sign is attached to the pole 110 feet above the ground, how far is he from the base of the pole, to the nearest foot?

11. Suggested Assignments Classwork: Workbook pg 215 1-22 Homework: pg 519-520 9-23