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  hcirc^\ hcirc )

\]

[ Leth me = calculate this743: \times \tan(22^\circ) ]

Using a calculator:

h=743×0.4040h = 743 \times 0.4040

h299.17h \approx 299.17

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