A boy 1.5 metres tall, sees the top of a building under construction at an elevation of 30°. The building is completed, adding 10 more metres to its height; and then the boy sees the top at an elevation of 60° from the same spot. What is the total height of the completed building?

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Solution

Let AB be the height of the child.

Let EC be the height of under constructed building and FC be the height of the complete building.

Let ∠EAD be the angle of elevation made by the boy’s eye while seeing the under constructed building.

Let ∠FAD be the angle of elevation made by the boy’s eye while seeing the completed building.

Let BC be the distance between the building and the child.

Let ED = x m and BC = y m

The figure for the given situation with dimensions can be made as follows:

In ΔAED:

Now in ΔAFD:

From equation (1) and equation (2), we get:

∴ Total height of the completed building = (10 + x + 1.5) m

≈ (10 + 4.96 + 1.5) m

= 16.46 m

Thus, the total height of the completed building is approximately equal to 16.46 m.

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