Question

an airplane takes off from point a in a straight line, as shown in the diagram. the distance from a to e is \boxed{} feet. (diagram shows: ad = 5,200 feet, ab = 5,600 feet, ac = 7,000 feet, with bd and ce perpendicular to ae)

Explanation:

Step1: Identify similar triangles

Triangles \(ABD\) and \(ACE\) are similar (right triangles, shared angle at \(A\)).

Step2: Set up proportion

\(\frac{AB}{AC} = \frac{AD}{AE}\) → \(\frac{5600}{7000} = \frac{5200}{AE}\)

Step3: Solve for \(AE\)

\(AE = \frac{5200 \times 7000}{5600} = 6500\)

Answer:

6500