ariamontogomery4
ariamontogomery4 ariamontogomery4
  • 14-04-2021
  • Mathematics
contestada

a guidebook says this tower is 50m tall.Is that correct? given deegrees are 27° and 46°
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a guidebook says this tower is 50m tallIs that correct given deegrees are 27 and 46 class=

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sqdancefan
sqdancefan sqdancefan
  • 14-04-2021

9514 1404 393

Answer:

   yes

Step-by-step explanation:

The tower is about 50.1 meters tall. The guidebook is correct.

__

The distance from the base of the tower to the angle vertex is ...

  d1 = h/tan(46°)

  d2 = d1 +50 = h/tan(27°)

Then the height of the tower is ...

  h/tan(46°) +50 = h/tan(27°)

  50 = h(cot(27°) - cot(46°))

  h = 50/(cot(27°) -cot(46°)) ≈ 50/(1.96261 -0.96569) ≈ 50/0.99692

  h ≈ 50.1544 . . . meters

The tower is more than 50 meters high.

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