Answer:
The height of the beam is: [tex]h=12\: feet[/tex]
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:
[tex]d_{beam}=15-6=9\: feet[/tex]
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.
[tex]15^{2}=9^{2}+h^{2}[/tex]
[tex]h^{2}=15^{2}-9^{2}[/tex]
[tex]h=\sqrt{15^{2}-9^{2}}[/tex]
Therefore, the heigh of the beam is:
[tex]h=12\: feet[/tex]
I hope it helps you!
