Math Problem Statement
From a hot-air balloon, Adriel measures a 22degrees∘ angle of depression to a landmark that’s 743 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Solution
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need- to The find horizontal the distance vertical to height the.
landmark### is Step ** 7431 feet:** Identify. the- known The values angle of- depression ** isAngle ** of22 depression°****:. (- The22 vertical^\ heightcirc (\ () h- \ ))Horizontal is distance the side: opposite ( the angle743 of \ depression).
feetUsing the- ** tVerticalangent distance** function (:
(\ h[ \t))an is(\ whattheta we) need = to \ findfrac.
{\Usingtext the{ **optpositeangent}} function{**text:
{\adj[ acent\t}} an(]
thetaSub)stit =uting \ thefrac given{\ valuestext:
{\op[ posite\t}}an{(text22{^\adjcircacent)}} =\ ]
frac{[ h\t}{an743(} 22^]
circSol)ving = for \ (frac h{ \h):
}{\743[ } h\ =]
###743 Step \ times2 :tan Solve( for22 )
\]
[ Leth me = calculate this743: \times \tan(22^\circ) ]
Using a calculator:
Final Answer:
The balloon’s vertical distance above the ground is 299.The17 balloon feet's vertical.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Tangent Function
Formulas
tan(θ) = opposite/adjacent
Theorems
Right Triangle Trigonometry
Suitable Grade Level
Grades 8-10
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