Advanced Geometry 9 .10 Trigonometric Ratios Angles of Elevation & Depression

1. Advanced Geometry9 .10 Trigonometric Ratios Angles of Elevation & Depression Objective: To use angles of elevation and depression to solve problems.

2. s of Elevation and Depression horizon Angle of depression (Looking DOWN from the horizon) (Looking UP from the horizon) Angle of elevation horizon

3. Angles of Elevation • The angle of elevation of an object as seen by an observer is the angle between the horizon and the line from the object to the observer's eye (the line of sight). Object Line of sight Angle of elevation horizon Observer’s eye

4. Angle of Depression • If the object is below the level of the observer, then the angle between the horizon and the observer's line of sight is called the angle of depression Observer’s eye horizon Angle of depression Line of sight Object

5. Ex.1:  of Elevation Problem Bob is standing 80m from the base of a building. When he looks up at a 25 angle he sees the top of the building. What is the height of the building? h opp tan 25° = 80m adj h is opposite (.4663) = __h__ 80 is adjacent 80m Toa is Tangent h 37.3m (.4663)(80) = h Height ≈ 37.3m 25° horizon 80

6. Ex.2:  of Depression Problem • A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35. The lamppost is 14ft tall. How far away is the observer from the bird? Sin 35 = 14 14 is opposite x x is hypotenuse (.5736) = 14 35 Soh is Sine x (.5736)x = 14 x 14ft 14ft x = 14/(.5736) x ≈ 24.4ft 35

7. Ex.3: Finding the angle • An airplane is flying at a height of 2 miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport? 2 2 is opposite 5 Toa is Tangent 5 is adjacent x 22 tan x = tan x = 0.4 2 miles 2 miles x = (tan-1) 0.4 x ≈ 22⁰ Airport x 5 miles 5 miles

8. 9.10 Assignment P 425 (2; 4 – 8; 10, 11, 13, 15)