there is an airplane flying in the sky, and you are ... · there is an airplane flying in the sky,...

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There is an airplane flying in the sky, and you are curious about how high it is off the ground. You have a special tool for measuring angles, called a goniometer. Your goniometer tells you that your viewing angle from your eyes, which are 5 feet off the ground, is 30 degrees. Your laser tape measure also tells you that the distance between you and the plane is 8,000 feet. 30° How high off the ground is the airplane? (Remember how high your eyes are from the ground!!)

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Page 1: There is an airplane flying in the sky, and you are ... · There is an airplane flying in the sky, and you are curious about how high it is off the ground. You have a special tool

Thereisanairplaneflyinginthesky,andyouarecuriousabouthowhighitisofftheground.Youhaveaspecialtoolformeasuringangles,calledagoniometer.Yourgoniometertellsyouthatyourviewinganglefromyoureyes,whichare5feetofftheground,is30degrees.Yourlasertapemeasurealsotellsyouthatthedistancebetweenyouandtheplaneis8,000feet.

30°

Howhighoffthegroundistheairplane?(Rememberhowhighyoureyesarefromtheground!!)

Page 2: There is an airplane flying in the sky, and you are ... · There is an airplane flying in the sky, and you are curious about how high it is off the ground. You have a special tool

Thereisanairplaneflyinginthesky,andyouarecuriousabouthowfarawaytheplaneisfromyou.Youhaveaspecialtoolformeasuringangles,calledagoniometer.Yourgoniometertellsyouthatyourviewinganglefromyoureyesis45degrees.Yourlasertapemeasurealsotellsyouthatthedistancebetweenyouanddirectlybelowtheplaneis4,000feet.

?? 4,000ft 45°

Howfarfromyouistheairplane?

Page 3: There is an airplane flying in the sky, and you are ... · There is an airplane flying in the sky, and you are curious about how high it is off the ground. You have a special tool

TODOTHISTASK,YOUWILLNEEDTOEITHERBEABLETOTYPEINVERSETRIGINTOYOURCALCULATOR(ex:sin$% button)oryouwillneedtoclickonthisLINK(http://www.calculatorsoup.com/calculators/trigonometry/inversetrigonometricfunctions.php)tofindtheanswer.***sin$%alsomeansarcsin.Thisappliestocosineandtangent,aswell.Thereisanairplaneflyinginthesky,andyouarecuriousabouttheviewinganglebetweenyouandtheplane.Youhaveaspecialtoolformeasuringangles,calledagoniometer,butitisbroken,soyouneedtofigureitoutonyourown.Yourlasertapemeasuretellsyouthatthedistancebetweenyouanddirectlybelowtheplaneis4,000feetandthedistancebetweentheplaneandthegroundis10,005feet.(Remember:youreyesare5feetofftheground!!)

10,005ft 4,000ft ???

Whatistheviewinganglefromyoutotheairplane?

Page 4: There is an airplane flying in the sky, and you are ... · There is an airplane flying in the sky, and you are curious about how high it is off the ground. You have a special tool

Notesneededtoaccomplishthistask:Forrighttriangles:

sin 𝐴 = ,--,./0123-,0145.1

cos 𝐴 = 89:8;14023-,0145.1

tan 𝐴 = ,--,./0189:8;140

𝐴 = sin$% ,--,./0123-,0145.1

; 𝐴 = cos$% 89:8;14023-,0145.1

; 𝐴 = tan$% ,--,./0189:8;140

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