SOLUTION: Inside a semi circular tunnel of diameter of 22 feet, a vertical support beam is placed 5 feet from the side of the tunnel. How tall is the beam?

Question 313332: Inside a semi circular tunnel of diameter of 22 feet, a vertical support beam is placed 5 feet from the side of the tunnel. How tall is the beam?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

The support beam is 5 feet from the end. from the ground.
The ground of the tunnel is the diameter of the tunnel.
the radius of the tunnel = 11 feet
so it is 5 feet from the center.
Let the center be O.
The point where the beam touches the ground be B
The beam touches the circumference of the tunnel at P
Angle OBP is a right angle
..
OBP is a right triangle
Leg OB = 6feet
Hypotenuse OP = radius of circle = 11feet
op^2-OB^2= leg^2
11^2-6^2= Leg ^2
121-36=leg^2
85= leg^2
sqrt85 = leg of the triangle
=9.22 feet. This is the height of the beam.
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