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From a hot-air balloon, Guadalupe measures a 31 degree angle of depression to a landmark thats 316 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary

From a hot-air balloon, Guadalupe measures a 31 degree angle of depression to a landmark thats 316 feet away, measuring horizontally. What’s the balloon’s verti class=

Answer :

We will first sketch the problem

Let x be the vertical distance above the ground

Using the trigonometric ratio;

[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan 31=\frac{x}{316}[/tex]

cross-multiply

[tex]x=316\tan 31^o[/tex][tex]x\approx189.9[/tex]

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