You live in the building on the left in the drawing, and a friend lives in the o

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 21° above the horizontal, whereas your line of sight to the base of the other building makes an angle of 52° below the horizontal. Determine the ratio of the height of the taller building to the height of the shorter building. State whether your friend is right or wrong

Explanation / Answer

Let y be the height of your building, x be the difference in heights, and d be the horizontal distance between the two buildings.

Then,

tan(theta_1) = x/d
tan(theta_2) = y/d

So,

x/y = tan(theta_1)/tan(theta_2) = tan(21)/tan(52)

= 0.3 approx

Height of your friend's building/Height of your building = (y+x)/y = 1 + x/y

= 1.3

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