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

Distance from Ahmad at DDD to the wall at BB is 10.5 m.
Ahmad's height DE = 1.6DE=1.6 m.
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Distance from the spotlight at AA to Ahmad at DDis 22 m.

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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:

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

Using similar triangles:

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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