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Day 3 – Solving Right Triangles and Angles of Elevation and Depression

!No!Angles!

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Solving!Right!Triangles!

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Example!1!Find!the!measures!of!angle!A!and!C.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!8!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!A!!!!!!!!!!!!!!!!!!!5!!!!!!!!!!!!!!!!B!!!!!!!!!!!!!!!!!!!!!!!!

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How!can!you!find!AC?!!!!!

Example!2!Solve!the!triangle!below.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!A!!!!!!!!!!!!!!!!!!3!!!!!!!!!!!!!!!!B!!!!!!!!!!!!!!!!!!!!!!!

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Example!3!(You!Try)!Find!all!unknown!measures.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!12!10!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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Example!4!(You!Try)!!Solve!the!Triangle!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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Angle!of!Elevation!

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Angle!of!Depression!

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Example!5!Classify!the!each!angle!as!an!angle!of!elevation!or!depression.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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53o!

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3

1

2

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Example!6!When!the!angle!of!elevation!to!the!sun!is!37°,!a!flagpole!casts!a!shadow!that!is!24.2!ft!long.!!What!is!the!height!of!the!flagpole!to!the!nearest!foot?!!!

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Example!7!The!pilot!of!a!traffic!helicopter!sights!an!accident!at!an!angle!of!depression!of!18°.!!The!helicopter’s!altitude!is!1560!ft.!!What!is!the!horizontal!distance!from!the!helicopter!to!the!accident?!!!

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Solve the Triangles

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Angle of Elevation and Depression Practice

1.! An'air'traffic'controller'at'an'airport'sights'a'plane'at'an'angle'of'elevation'of'41o.''The'pilot'reports'that'the'plane’s'altitude'is'4000'feet.''What'is'the'horizontal'distance'between'the'plane'and'the'airport?'

2.! A'forest'ranger'in'a'90'foot'observation'tower'sees'a'fire.''The'angle'of'depression'to'the'fire'is'7o.'What'is'the'horizontal'distance'between'the'tower'and'the'fire?'

3.! From'the'top'of'a'building'42'feet'high,'the'angle'of'depression'to'a'car'stopped'on'the'ground'is'27o.''What'is'the'distance'from'the'car'to'the'base'of'the'building?'

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4.! Tess'is'installing'a'support'wire'from'a'point'on'the'ground'to'the'top'of'a'tree.''The'angle'of'elevation'to'the'top'of'a'tree'is'75o.''If'the'wire'is'10'feet'long,'how'far'Tess'from'the'tree?''

5.! A'man'on'top'of'a'94'foot'cliff'spots'his'friend'on'the'ground'below'at'an'angle'of'depression'of'10o.''What'is'the'horizontal'distance'between'the'man'and'his'friend?'

6.! A'kite'is'50'meters'high'when'200'meters'of'string'is'out.''What'angle'does'the'kite'make'with'the'ground?'

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Extra Practice 1) 2) 3)

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4) 5)

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