Question

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?

Answer 1

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!