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

Question

You live in the building on the left in the drawing below, 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 the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle ?1 = 29° above the horizontal, while your line of sight to the base of the other building makes and angle ?2 = 43° below the horizontal. Determine the ratio of the height of the taller building to the height of the shorter building

Explanation / Answer

ratio is (tan29 + tan43)/tan43 = 1.5944 let height of shorter buliding is h1 height of taller building is h1+h2 seperation between them is b tan29 = h2/b tan43 = h1/b so ratio is h1+h2/h1 = 1.5944

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