Question

an aerial camera is suspended from a blimp and positioned at d. the camera needs to cover 125 meters of ground distance. if the camera hangs 10 meters below the blimp and the blimp attachment is 20 meters in length, at what altitude from d to b should the camera be flown?
(options: 31.25 m, 62.5 m, 150 m, 250 m)

Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle DEF \) and \( \triangle DBC \) are similar (by AA similarity, as they share a right angle and the same angle at \( D \)).

Step2: Set Up Proportion

Let \( h \) be the height from \( D \) to \( B \). The ratio of corresponding sides in similar triangles is equal. So, \( \frac{DE}{DB} = \frac{EF}{BC} \). We know \( DE = 10 \, \text{m} \), \( EF = 20 \, \text{m} \), and \( BC = 125 \, \text{m} \). Plugging in, we get \( \frac{10}{h} = \frac{20}{125} \).

Step3: Solve for \( h \)

Cross - multiply: \( 20h = 10\times125 \). Then \( 20h = 1250 \). Divide both sides by 20: \( h=\frac{1250}{20}=62.5 \, \text{m} \).

Answer:

\( 62.5 \, \text{m} \)