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!!)

Transcript of There is an airplane flying in the sky, and you are ... · There is an airplane flying in the sky,...

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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