Question

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1. the foot of a ladder is 1.2 m from a fence that is 1.8 m high. the ladder touches the fence and rests against a building that is 1.8 m behind the fence. draw a diagram, then determine the height on the building reached by the top of the ladder.

Explanation:

Step1: Identify Similar Triangles

The fence and the building are vertical, and the ground is horizontal, so the triangles formed by the ladder, ground, and fence (small triangle) and ladder, ground, and building (large triangle) are similar. Let the height on the building be \( h \) meters. The base of the small triangle is \( 1.2 \) m, and the base of the large triangle is \( 1.2 + 1.8=3 \) m. The height of the small triangle is \( 1.8 \) m.

Step2: Set Up Proportion for Similar Triangles

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{1.8}{1.2}=\frac{h}{3}\).

Step3: Solve for \( h \)

Cross - multiply: \( 1.2h = 1.8\times3 \). Calculate \( 1.8\times3 = 5.4 \). Then, \( h=\frac{5.4}{1.2}=4.5 \) meters.

Answer:

The height on the building reached by the top of the ladder is \( 4.5 \) meters.