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a person in a hot air balloon sights two cities, one behind other. The angles of depression of the cities are 45 degrees and 30 degrees. If the hot air balloon is 750 m high, how far apart are the two cities?
Let distance between two cities = x Let C₂ = distance from farther city from the sight at 30 degrees Let C₁ = distance from nearer city from the sight at 45 degrees Height from the ground to air balloon = 750 m
Distance from below the balloon to the farther city (C₂):
tan 30⁰ = [tex] \frac{750}{C _{2} } [/tex]
C₂ = [tex] \frac{750}{tan30} [/tex]
C₂ = [tex] \frac{750}{0.58} [/tex]
C₂ = 1,293 m
Distance from below the balloon to nearer city (C₁):
tan 45 = [tex] \frac{750}{C _{1} } [/tex]
C₁ = [tex] \frac{750}{tan45} [/tex]
C₁ = [tex] \frac{750}{1} [/tex]
C₁ = 750 m
Distance (x)between two cities:
x = C₂ - C₁
x = 1,293 m - 750 m
x = 543 m
ANSWER: The distance between two cities are 543 meters.
Please click image below for my solution with illustration.
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