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The roof of one building is 400 feet below the roof of another building. A person standing on the lower roof sees another person standing on the higher roof at a 35o angle of elevation. Approximately how far apart are the buildings? Round to the nearest foot.

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oladayoademosu

Since the roof of one building is 400 feet below the roof of another building, the buildings are 571 ft apart.

The required triangle

The line of sight of the lower building to the taller building, the distance of the buldings apart, D and the height of the lower building below the taller building, h form a right angled triangle with angle Ф = 35° = angle of elevation of taller building and opposite side, h.

From trigonometric ratios, we have that

tanФ = h/D

So, D = h/tanФ

Since

  • h = 400 ft and
  • Ф = 35°,

Distance of building apart

Substituting the values of the variables into the equation, we have

D = h/tanФ

D = 400 ft/tan35°

D = 400 ft/0.7002

D = 571.27 ft

D ≅ 571 ft to the nearest foot

So, the roof of one building is 400 feet below the roof of another building, the buildings are 571 ft apart.

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