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A hot air balloon is ascending with you in the balloonas a friend is filming your ride. The friend is 50 awayfrom where the balloon took off. When your friendfirst starts filming your ride her camera is at a 30 degreeangle. After a minute her camera is at a 70 degreeangle. How far did you travel in that minute? What isthe speed in feet per minute?70°Yourfriend30050 footFigure 4.104 Ascending in a hot-airballoon

Sagot :

After a minute her ballon is at 70 degrees. How far he traveled in a minute is calculated as y - x. Therefore,

[tex]\begin{gathered} \tan 30=\frac{x}{50} \\ x=50\tan 30 \\ x=50\times0.57735026919 \\ x=28.8675134595 \\ x=28.87 \end{gathered}[/tex][tex]\begin{gathered} \tan 70=\frac{y}{50} \\ y=50\tan 70 \\ y=137.373870973 \\ y=137.37\text{ ft} \end{gathered}[/tex]

How far he travel in a minute = 137.37 - 28.87 = 108.5 ft

b. The speed in feet per minute can be calculated below

[tex]\text{speed}=\frac{108.5}{1}=108.5ft\text{ per minute}[/tex]

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