8.5 Angles of Elevation and Depression Then: You used similar triangles to measure distances indirectly. Now: 1. Solve problems involving angles of elevation and depression. 2. Use angles of elevation and depression to find the distance between two objects. http://mathblog.files.wordpress.com/2008/05/8-4definition.png

Angle of elevation Angle formed by a horizontal line and an observer’s line of sight to an object above the horizontal line. http://resource.rockyview.ab.ca/t4t/math10c/images/m1/m10c_m1_110_opt.jpeg

Angle of Depression Angle formed by a horizontal line and an observer’s line of sight to an object below the horizontal line. http://resource.rockyview.ab.ca/t4t/math10c/images/m1/m10c_m1_111_opt.jpeg

Example of Definitions: Name the angle of elevation and the angle of depression in each figure. a. b.

Example 1: Angle of Elevation The angle of elevation from point A to the top of a hill is 49. If point A is 400 feet from the base of the hill, how high is the hill?

Example 1: Angle of Elevation Find the angle of elevation of the sun when a 12.5 meter tall telephone pole casts an 18 meter long shadow.

Example 2: Angle of Depression A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.

Example 2: Angle of Depression From the top of a 120 foot high tower, an air traffic controller observes an airplane on the runway at an angle of 19. How far from the base of the tower is the airplane?

Example 3: Use Two Angles of Elevation or Depression To estimate the height of a garage, Jason sights the top of the garage at a 42 angle of elevation. He then steps back 20 feet and sites the top at a 10 angle. If Jason is 6 feet tall, how tall is the garage to the nearest foot?

Example 3a: Solve for AC, then AB, then add in eye height. 1). Find mDCA and m DAC 2) Find AC:

Example 3a: 3. Find AB: 4. Find the height of the building

Example 3: Use Two Angles of Elevation or Depression Susan stands on the ground and sights to the top of a steep cliff at a 60 angle of elevation. She then steps back 50 meters and sights to the top of the steep cliff at a 30 angle. If Susan is1.8 meters tall, how tall is the steep cliff to the nearest meter?

Example 3b: Solve for the height of the cliff:

p. 583-587 #4-8 all, 10-20 evens, 28-32 all, 34-38 evens 8.5 Assignment p. 583-587 #4-8 all, 10-20 evens, 28-32 all, 34-38 evens