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vesna_86 [32]
3 years ago
9

Inside a semicircular tunnel of diameter 30 feet, a vertical support beam is placed 6 feet from the side of the tunnel. How tall

is the beam?
Mathematics
1 answer:
adell [148]3 years ago
8 0

Answer:

The height of the beam is: h=12\: feet

Step-by-step explanation:

The radius of the tunnel is r = 15 feet

The distance of the beam from the center of the tunnel is:

d_{beam}=15-6=9\: feet

We have a right triangle, where:  

  • The Hypotenuse is 15 feet
  • One side is 9 feet
  • The other side is the height of the beam

Let's use Pythagoras theorem.

15^{2}=9^{2}+h^{2}

h^{2}=15^{2}-9^{2}

h=\sqrt{15^{2}-9^{2}}

Therefore, the heigh of the beam is:

h=12\: feet

I hope it helps you!

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