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Day 6: Angles of Depression and Elevation Unit 5: Trigonometric Functions

+Warm Up

10 minutes

End

n  Find the missing side length

1) 2)

n  Find the missing angle

3) 4)

+Homework Check

+Today’s Objective

n Students will define and apply Angles of Depression and Elevation to solve word problems.

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n The angle of elevation is the angle formed by a horizontal line (ground) and the line of sight looking up.

Angle of Elevation

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n The angle of elevation is the angle formed by a horizontal line (sky) and the line of sight looking down.

Angle of Depression

+Angle of Depression

The Angle of Depression is the angle from the “sky to the

line”

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n Notice … the angle of elevation and the angle of depression are congruent angles when in the same picture!

+Extension – How tall is it??

n  There’s a light out on the very top of the WRAL tower and it needs to be replaced!

n  How high up do you need to go to get to the top?

n  Standing in the Papa Johns parking lot, you are 220.5 feet from the base of the tower.

n  You measure that the angle from the ground to the top of the tower is 53.7º.

n  Can you find the height?

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x

220.5 ft

53.7º

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2o

2o angle of elevation

angle of depression

Suppose an operator at the top of a lighthouse sights a sailboat on a line that makes a 2o angle with the horizontal line. If the top of the lighthouse is 25m above sea level, what is the distance x between the boat and the base of the lighthouse to the nearest integer?

25

x

+ALWAYS DRAW A PICTURE!!!

1.  Sally is holding a kite 4 feet off the ground. The kite is on a 40-foot string and has an angle of elevation of 50º. How high above the ground is the kite?

2.  From the top of a tower, the angle of depression to a stake on the ground is 72º. The top of the tower is 80 feet above ground. How far is the stake from the foot of the tower?

+3.  A tree 40 feet high casts a shadow 58

feet long. Find the measure of the angle of elevation of the sun.

4.  A ladder leaning against a house makes an angle of 60º with the ground. The foot of the ladder is 7 feet from the foundation of the house. How long is the ladder?

+How Tall is the School?

n  Imagine you are a team of surveyors which needs to find out the height of our school building in order to sign clearance forms approving new construction on it. How could you use trigonometry to find the height, without having to measure from the bottom of the school to the top with a tape measure?

+Using Trig to Find the Height

n  The device a surveyor would use to complete this task is called a clinometer. Fortunately, the new iPhone software comes with its very own Clinometer in the Compass App! Here are your instructions:

Choose your team roles n  Quality Assurance Manager – Reads all instructions and double checks on

measurements and recordings to assure accurate results. n  Angle Measurer – Uses iPhone to determine any angles n  Length Measurer – Uses tape measure to find any distances n  Recorder – Records all measurements and information

n  1. Open the compass app on your iphone and swipe left. Experiment with what happens when you lay the iPad flat and when you hold it up. We want to check for angles so we will be holding it up.

n  2. When measuring angles, you will need to align the long side of the iphone with your eye. While one group member uses the iphone, another member should record the angles. If you are getting negative numbers, turn the iphone around.

n  3. As a group, fill out this worksheet. Once your group is finished, submit your results to the construction contractor, Mr. Koberstein.

+And the correct Height is….

+Poster Activity

As a group, create a poster diagram to represent the activity you just completed. You must include the following information: n  A right triangle n  A picture of the Angle Measurer n  The school n  All measurements found (including the height of the angle measurer) n  Your Trigonometric Proportion n  Your work to solve the proportion n  Your final answer circled or in a box n  Color

+Independent Practice

n Angles of Depressions and Elevation worksheet

n Quiz Tomorrow