Thereisanairplaneflyinginthesky,andyouarecuriousabouthowhighitisofftheground.Youhaveaspecialtoolformeasuringangles,calledagoniometer.Yourgoniometertellsyouthatyourviewinganglefromyoureyes,whichare5feetofftheground,is30degrees.Yourlasertapemeasurealsotellsyouthatthedistancebetweenyouandtheplaneis8,000feet.
30°
Howhighoffthegroundistheairplane?(Rememberhowhighyoureyesarefromtheground!!)
Thereisanairplaneflyinginthesky,andyouarecuriousabouthowfarawaytheplaneisfromyou.Youhaveaspecialtoolformeasuringangles,calledagoniometer.Yourgoniometertellsyouthatyourviewinganglefromyoureyesis45degrees.Yourlasertapemeasurealsotellsyouthatthedistancebetweenyouanddirectlybelowtheplaneis4,000feet.
?? 4,000ft 45°
Howfarfromyouistheairplane?
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?
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
hypotenuseopposite
adjacentopposite
oppositeopposite
A