Greenwood press
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book-20600
Mathematical Concepts
▲ ▼ ▲ Restructuring the angles in an intersection to make turning a vehicle easier. initial street design restructured street design The amount of space, s, saved by using right-angled spaces is s = −l cos α for each row in the parking lot, where l is the length of the space and α is the angle of the turn into the space. When the shape of a space is transformed from a rectangle (right-angled) to a parallelogram (obtuse-angled), the extra horizon- tal distance needed in a parking-lot row will be the amount of space that the last car displaced from its previous perpendicular arrangement. In the obtuse-angled situation, the length of the parking space is the hypotenuse of a right triangle formed with the curb. The cosine of the angle between the curb and the parking lines, cos θ, is the ratio of the horizontal curb space, s, to the length of the park- ing space, l. In an equation, this is written as cos θ = s l . Multiplying both sides of the equation by l will change it to s = l cos θ. The angle against the curb and the car’s turning angle are supplementary, because the curb and car’s path are parallel. The interior angles on the same side of the trans- versal (the parking lines) are supplementary, so cos θ = − cos α. Substituting this result into s = l cos θ generates the equation, s = −l cos α. If the parking lines were at a 60° angle with the curb, the turning angle would be 120°. Suppose the dimensions of a parking space are 8 feet by 20 feet. If the lot is transformed from right-angled spaces to oblique-angled spaces, each row would lose s = −20 cos 120 ◦ = 10 feet, which is equivalent to a little more than one space! Download 1.81 Mb. Do'stlaringiz bilan baham: |
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