SOLUTION: Inside a semicircular tunnel of diameter 20 feet, a vertical support beam is placed 6 feet from the side of the tunnel. How tall is the beam? I tried using the pythagorean theo

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Question 136990: Inside a semicircular tunnel of diameter 20 feet, a vertical support beam is placed 6 feet from the side of the tunnel. How tall is the beam?
I tried using the pythagorean theorem. Since the beam hits the diameter at a 90 degree angle. I use 6^2+x^2=90^2
I did not get any of the choices. I guessed by looking at the picture that the answer is less than the diameter but greater that the distance from the side. I got 9.2 ft.
Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
a triangle inscribed in a semicircle is a right triangle, with the diameter as the hypotenuse

the beam divides the large triangle (ends of diameter and top of beam) into two smaller triangles
__ these smaller triangles are similar to the large triangle (and also to each other)

let x="height of beam" __ using ratios of similar triangles __ x:6::14:x

x/6=14/x __ "cross" multiplying __ x^2=84 __ x=sqrt(84)