![]() GIVEN – Understand the given information – TRANSLATE and VISUALIZE: TIP: Simultaneous translation will help you understand a question in thorough detail and leave no scope for confusion as you progress through the solution. This way, we’ll clearly get all that is given to us and that we need to find. We will translate the question from English to Math as we read it. choose (B)!įrom a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big worse case you have a 1/3 shot at picking up the points. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).įinally: AB=8, so the correct answer is 8. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. The answer to the question will, therefore, be the height AB. ![]() Let's label the point at which the line intersects the circle B. Now draw a line straight up from A to the top of the tunnel. Let's call the leftmost point on the base of the traffic lane A. We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10. ![]() Let's label the midpoint of the circle O. I'll try to explain as best as I can without drawing a diagram - sadly, I don't have the computer resources to do so (or at least I don't know how!). If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel? The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. ![]() The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. ![]()
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