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A man wants to measure the height of a nearby building. He places a 5 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by
the shadow of the building. The total length of the building's shadow is 167 ft, and the pole casts a shadow that is 4.5 ft long, How tall is the building? Round
your answer to the nearest foot. (The figure is not drawn to scale.)
Building
Х
$
Pole
Shadow of pold
Shadow of building

A man wants to measure the height of a nearby building He places a 5 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by class=

Respuesta :

The height of the building to the nearest foot is 186 feet.

The situation form two similar right triangle.

Properties of right triangle:

  • One of its angle is 90 degrees.
  • The angles and sides can be found using trigonometric ratios.

Similar triangles:

Similar triangle are not necessarily the same size. There corresponding angles are the same. The corresponding sides are a ratio. Therefore, we will establish a ratio of the triangles.

x = height of the building

Using similar triangle ratio:

  • 5 / x = 4.5 / 167

5 / x = 4.5 / 167

cross multiply

167 × 5 = 4.5x

4.5x = 835

x = 835 / 4.5

x = 185.555555556

x = 186 ft.

learn more on right triangle here:https://brainly.com/question/1076462?referrer=searchResults

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