Angles of Elevation and Depression Unit 5-5 Trig word problems

Who may use these?  Pilots and air traffic controllers use angles of depression to calculate distances.  These people are trained both in civilian and military environments  Beginning pay for pilots is $73,000  Beginning pay for air traffic controllers $92,000  These positions in the military require at least an 84 on the ASVAB Real world uses

Angle of elevation---is the angle formed by a horizontal line and a line of sight to a point above the line. Angle of elevation Altitude of plane ground Pilot’s horizontal line Pilot’s line of sight Real world uses

Angle of depression---is the angle formed by a horizontal line and a line of sight to a point below the line. Angle of depression Altitude of plane ground Pilot’s horizontal line Pilot’s line of sight Real world uses

Notice that the angle of elevation and depression are ______________ ___________ ______________ of the parallel lines (with the line of sight as the transversal)……and so these two angles are _______________ Draw pictures to help you visualize the right triangles (A well draw picture is a half solved math problem) Definitions

Classify each angle as an angle of elevation or depression Example #1

A forest ranger in a 90 foot observation tower sees a fire. The angle of depression to the fire is 7 o. What is the horizontal distance between the tower and the fire? 90 ft 7o7o 7o7o x h o a Which function? TANGENT Example #2

A pilot flying at an altitude of 2.7 km sights two control towers directly in front of her. The angle of depression to the base of one tower is 37 o. The angle of depression to the base of the 2 nd tower is 58 o. What is the distance between the towers? 37 o 58 o 2.7 km 37 o 58 o Example #3

Graph the triangle, then find the lengths of the sides, then find the angle measures using trig functions. A (-2, -4) B (3, 3) C ( -2, 3) Example #4

Show your work here!!! Example #4

To attract customers to his store, Mike has a large American flag waving high above his parking lot. With the sun directly overhead, the shadow of the flag falls 12 feet from the bottom of the flag pole. Mike sights an angle of elevation of 50 o. Find the height of the flag pole. Draw a picture for help. The wind picks up, and the sun moves into the western sky. The length of the shadow changes to 18 feet from the bottom of flag pole. If Mike is standing in the same place as before, what is his current angle of elevation? Use can use the same picture, just change the shadow. Example #5 and #6

Show your work here!!! Example #5 and #6