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?

Answer 1

The camera should low by 12 meters

Answer 2

The camera should low by 12 meters

Explanation:

* Lets explain how to solve the problem

- From the figure:

# The length of the camera is represented by FE

∴ EF = 20 meters

# The ground distance covered by the camera represented by AC

∴ AC = 125 meters

# The camera will be flown at an altitude represented by DB

∴ DB = 75 meters

# The altitude should the camera hanged below the blimp

represented by GD

∴ Find the length of GD

* Lets solve the problem

- In the two triangles ADC and EDF

∵ EF // AC

∴ m∠A = m∠E ⇒ alternate angles

∴ m∠C = m∠F ⇒ alternate angles

∵ m∠ADC = m∠EDF ⇒ vertical angles

∴ Δ ADC ≈ Δ EDF ⇒ AAA similarity

∴ Their corresponding sides are proportions

∴ AC/EF = AD/ED = CD/FD = constant ratio

∵ AC = 125 and EF = 20

∴ The constant ratio is 125/20 = 25/4

∵ Their Altitudes have the same ratio of their corresponding sides

∵ BD is the altitude of Δ ADC and GD is the altitude of Δ EDF

∴ BD/GD = 25/4

∵ BD = 75

∴ 75/GD = 25/4

- Use cross multiplication to find GD

∴ 25 GD = (75)(4)

∴ 25 GD = 300

- Divide both sides by 25

∴ GD = 12

∴ The camera should low by 12 meters