A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his
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Step-by-Step Solution
Step 1: Understand the Geometry and Set up Variables
First, let's visualize the situation. The boy is 1.5 m tall, and the building is 30 m tall. Since the angle of elevation is measured from the boy's eyes, we need to consider the effective height of the building above his eye level. This is the total height of the building minus the boy's height.
Step 2: Calculate Effective Height
The effective height of the building from the boy's eye level is 28.5 m. Let x be the initial distance of the boy from the building and y be the distance he walked towards the building. So, the final distance from the building will be x-y.
Step 3: Apply Tangent for Initial Position
When the angle of elevation is 30∘, the boy is at an initial distance x from the building. We can use the tangent function, which relates the opposite side (effective height) to the adjacent side (distance from the building). We know that tan(30∘)=31.
Step 4: Apply Tangent for Final Position
As the boy walks y meters towards the building, his new distance from the building is x-y. The angle of elevation increases to 60∘. We apply the tangent function again. We know that tan(60∘)=3.
Step 5: Calculate the Distance Walked
To find the distance the boy walked, y, we subtract the final distance from the initial distance. We substitute the values we found for x and x-y and simplify. We can also approximate the value using 3≈1.732.