Question

1. image of a tree (ab) with height x ft, a person (de) with height 4 ft, distance from b to e is 9 ft, distance from e to c is 6 ft, forming similar triangles abc and dec

Explanation:

Step1: Identify Similar Triangles

Triangles \(ABC\) and \(DEC\) are similar (AA similarity, as both have right angles and share \(\angle C\)). So, their corresponding sides are proportional.

Step2: Set Up Proportion

The ratio of height to base for \(\triangle DEC\) is \(\frac{4}{6}\), and for \(\triangle ABC\) is \(\frac{x}{9 + 6}=\frac{x}{15}\). Since they are similar, \(\frac{x}{15}=\frac{4}{6}\).

Step3: Solve for \(x\)

Cross - multiply: \(6x = 4\times15\). Then \(6x = 60\). Divide both sides by 6: \(x=\frac{60}{6}=10\).

Answer:

The height of the tree \(x\) is \(10\) feet.