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Angle of Elevation The angle between a horizontal and a line of

sight above the horizontal is called an angle ofelevation.

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Example:If a 7 ft. !agpole casts a shadow of "# ft.long$ what is the angle of elevation of the s%nfrom the tip of the shadow&

'ol%tion: (et ) * angle of the elevation of thes%n. Th%s$tan ) * 7#+"#

tan ) , .9$  ) * Tan/ .9 , #9.071

 The angle of elevation of the s%n from the tipof the shadow is #9.071

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 Angle of 2epression The angle of depression is congr%ent to the

angle of elevation 3this ass%mes the ob4ect isclose eno%gh to the observer so that thehorizontals for the observer and the ob4ect aree5ectivel6 parallel this wo%ld not be the casefor an astrona%t in orbit aro%nd the earthobserving an ob4ect on the gro%nd.8

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Example:'%ppose an airplane begins its descent to a

r%nwa6 from an altit%de of $ ft.If the airplane is 7$ ft. from the r%nwa6 asmeas%red along the gro%nd$ what is the angleof depression&;se the fact that the meas%res of the angle ofelevation and the angle of depression are the

same. ;se the tangent f%nction to find ). Tan )*$+7$)* tan/ .#0,.7#1

 The angle of depression is .7#1

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<earing and =avigation=01E means the direction is 01 east of

north. The bearing to a point is the anglemeas%red in a cloc>wise direction from thenorth line.

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Example:An airplane ta>es o5 from =ino6 A?%ino International Airporton @ab%ha6 r%nawa6 which has a bearing of = #1E. After!6ing for miles$ the pilot t%rns 91 and heads toward thenorthwest. After the plane goes for " miles in this direction$what bearing has the plane from the terminal&'ol%tion:

After !6ing miles from the airport $ the plane is at B.After t%rning 91 toward the northwest and !6ing " miles$the plane is at @. In CB@$ ) obe6s the e?%ation tan)*"+* so tan / ,0. "1 The ac%te angle between north and ra6 @ is 0."1 - #1 *0. "1. The bearing of the plane from to @ is = 0."1 D.