You live in the building on the left in the drawing, and a friend lives in the o
ID: 2126517 • Letter: Y
Question
You live in the building on the left in the drawing, and a friend lives in the other building. The two of you are having a discussion about the heights of the buildings, and your friend claims that the height of his building is more than 1.50 times the height of yours. To resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of
You live in the building on the left in the drawing, and a friend lives in the other building. The two of you are having a discussion about the heights of the buildings, and your friend claims that the height of his building is more than 1.50 times the height of yours. To resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of ?1 = 20 degree above the horizontal, whereas your line of sight to the base of the other building makes an angle of ?2 = 38 degree below the horizontal.Explanation / Answer
Suppose the height of your building is Y, and the height of his building is Y + y, i.e. his building is y higher than yours. Also suppose that the distance between the buildings is x.
then tan 21 = y/x
and tan 52 = Y/x
Your friend says that his building is half again as tall as yours.
He is saying that (Y + y) / Y = 1.5
i.e. 1 + y/Y = 1.5
i.e. y/Y = 0.5
In fact y/Y = (y/x) / (Y/x) = tan 21 / tan 52 = 0.3
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