Do Now: 2. If tan (𝜃) = 2/5 find the exact values of the two remaining trigonometric functions for the acute angle 𝜃. (use the picture) 1. Find the exact value of the six trigonometric functions 20 29 𝜃 21

Angle of Elevation/Depression

Word problems What do we look for when solving word problems? What are some good ways to pick out key information? What should we do when working with word problems?

Vocabulary Some applications of trigonometry use an angle of elevation or depression. An angle of elevation is the angle formed by a horizontal line and observer’s line of sight to an object above . An angle of depression is the angle formed by a horizontal line and an observer’s line of sight to an object below.

Angle of Depression vs Angle of Elevation These angles are congruent because… Angle of depression Line of Sight Angle of elevation

Word Problems #1 A ground crew worker who is 6 feet tall is directing a plane 150 ft in the air on a runway. If the worker sights the plane at an angle of elevation 32°, what is the horizontal distance from the worker to the plane?

#2 A group of hikers on a camping trip climb to the top of a 1500-foot mountain. When the hikers look down at an angle of depression of 36°, they can see the campsite in the distance. What is the horizontal distance between the campsite and the group to the nearest foot?

#3 A hot air balloon that is moving above a neighborhood has an angle of depression of 28° to one house and 52° to a house down the street. If the height of the balloon is 650 feet, estimate the distance between the two houses.

Try this… What if a restaurant needed to build a wheelchair ramp for its customers? The angle of elevation for a ramp is recommended to be 5°. If the vertical distance from the sidewalk to the front door is two feet, what is the horizontal distance that the ramp will take up? How long will the ramp be? Round your answers to the nearest hundredth.

Try this… An inquisitive math student is standing 25 feet from the base of the Washington Monument. The angle of elevation from her horizontal line of sight is . If her “eye height” is 5ft, how tall is the monument?

Try this… A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?

Questions?