Ahmad stands at point D, 2m in front of a spotlight at point A. He is 1.6m tall and is facing the wall of a building which is 10.5m away from him. How tall (BC) is his shadow on the wall of the building

Explanation

Ahmad stands at point D, 2m in front of a spotlight at point A. He is 1.6m tall and is facing the wall of a building which is 10.5m away from him. How tall (BC) is his shadow on the wall of the building (5 marks)

To find the height $BC$ of Ahmad's shadow on the wall of the building, we can use the properties of similar triangles.

Given:

1. Ahmad's height $DE = 1.6$ m.
2. Distance from the spotlight at $A$ to Ahmad at $D$is $2$ m.
3. Distance from Ahmad at $D$ to the wall at $B$ is $10.5$ m.
4. Total distance $AB = 2 + 10.5 = 12.5$m.

Using similar triangles:

$$$$BCAB=DEAD​

Substitute the values:

$$frac{BC}{12.5} = frac{1.6}{2}$$ $$BC = 12.5 times frac{1.6}{2} = 12.5 times 0.8 = 10 text{ m}$$

Height $BC = 10$ m.

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