Question

type the correct answer in the box.
an airplane takes off from point a in a straight line, as shown in the diagram.
the distance from a to e is
feet.

Explanation:

Step1: Use similar triangles property

Since \(\triangle ABD\) and \(\triangle ACE\) are similar (by AA similarity, as \(\angle ABD=\angle ACE\) and \(\angle BAD = \angle CAE\)). The ratio of corresponding sides of similar triangles is equal. Let \(AE=x\). The ratio of the sides of the triangles is \(\frac{AB}{AC}=\frac{AD}{AE}\). Given \(AB = 5600\), \(AC=7000\), \(AD = 5200\).

Step2: Substitute values into the ratio formula

Substitute the values into \(\frac{AB}{AC}=\frac{AD}{AE}\), we get \(\frac{5600}{7000}=\frac{5200}{x}\). Cross - multiply: \(5600x=7000\times5200\).

Step3: Solve for \(x\)

First, simplify \(\frac{5600}{7000}=\frac{4}{5}\). So the equation becomes \(\frac{4}{5}=\frac{5200}{x}\), then \(4x = 5\times5200\), \(4x=26000\), \(x=\frac{26000}{4}=6500\).

Answer:

\(6500\)