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Unformatted text preview: Right Triangle Applications le g n A fE o on ti va le The angle of elevation or inclination is measured from a horizontal line looking up at something. The angle of depression or declination is measured from a horizontal line looking down at something. Example
Two buildings are on opposite sides of the street. The shorter building is 300 feet tall. The angle of elevation from the top of this building to the top of the taller building is 45º. The angle of declination from the top of the shorter building to the base of the taller is 30º. • How far apart are the buildings? • How high is the taller building? 45° 30° How can we find the distance x between the buildings? 300 300 tan 30 = x x 300 x= ≈ 519.6 tan 30 The distance between the buildings is approximately 520 ft. y 45° 30° How can we find the height if the second building?
y 300 300 520 45°
520 y tan 45 = 520 y 1= ⇒ y = 520 520 The taller building is 820 ft tall. Example
A tree casts a 60 foot shadow. The angle of elevation from the ground to the top of the tree is 30º. What is the height of the tree? How can we find the height of the tree?
h 30°
Shadow = 60 h tan 30 = 60 h = 60 tan 30 ≈ 34.6 The tree is approximately 35 ft tall. Example
An observer on top of a 60foot tall lighthouse sees a boat in distress at a 5º angle of depression. How far is the boat from the base of the lighthouse? How can we find the distance x?
5° 60 5° x 60 tan 5 = x 60 x= ≈ 685.8 tan 5 The boat is approximately 686 ft from the lighthouse. ...
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 Fall '08
 GARDNER
 Calculus, PreCalculus, horizontal line, taller building

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