Question

An aerial camera is suspended from a blimp and positioned at D. The camera needs to cover 125 meters of ground distance and will be flown at an altitude of 75 meters. If the camera attachment to the blimp is 20 meters in length, how low should the camera hang from the blimp, from G to D? Options: 1.7 m 10 m 12 m 33.3 m

Answer 1

Given:

From the given figure we have:

AC = 125 m = ground distance that the camera needs to cover

DB = 75 m = the altitude at which the camera should be flown

EF = 20 m = length of the camera attached to the blimp

To find:

How low should the camera hang from the blimp, from G to D?

Solution:

Let "GD" represent the altitude at which the camera is hanged from the blimp.

Considering ΔDEF & ΔDAC,

∵ EF // AC [as shown in the figure]

∠EDF = ∠ADC ..... [vertically opposite angles]

∠EFD =  ∠DCA ...... [alternate angles]

∠FED =  ∠DAC ..... [alternate angles]

∴ Δ DEF ~ Δ DAC ...... [By AAA similarity]

We know that the ratio of the corresponding altitudes of the two similar triangles is always equal to the ratio of their any two corresponding sides.

∴ $\frac{GD}{DB} = \frac{EF}{AC}$

By substituting DB = 75 m, EF = 20 m & AC = 125 m

$\implies \frac{GD}{75} = \frac{20}{125}$

$\implies GD = \frac{20 \:\times\: 75}{125}$

$\implies GD = \frac{1500}{125}$

$\implies \bold{GD = 12\:m}$

Thus, the camera should be hanged low by 12 m from the blimp, from G to D.

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