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 his building is half again as tall as 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, while your line of sight to the base of the other building makes an angle of 52° below the horizontal.




(a) Determine the ratio of the height of the taller building to the height of the shorter building.




(b) Determine whether your friend is right or wrong.

Explanation / Answer

let x be the distance between the bases of two buildings

H - height of the taller building
h - height of the smaller building

a)
then tan(21) = (H - h)/x
tan(52) = h/s

(H-h)/h = tan(21)/tan(52)
H/h = 1 + tan(21)/tan(52) = 1.3
b)
your friend is wrong

because H is 1.3 times that of h.

not  2 times as told by your friend

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