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

Question

3 years ago

9

is the beam?

1 answer:

adell [148] · Answer 1 · 2022-04-04T19:08:17+03:00

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:

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!