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Geometry word problems? |
Okay I need help with these three word problems please: In slow-pitch softball, the distance between consecutive bases is 65 feet. The pitcher's plate is located on a line between second base and home plate, 50 feet from home plate. How far is the pitcher's plate from second base? Justify your answer. The distance of the base of a ladder from the wall it leans against should be at least 1/4 of the ladder's total length. Suppose a 10 foot ladder is placed according to these guidelines. Give the minimum distance of teach? Explain. You want to hang a painting 3 feet from the a hook near the ceiling of an art gallery. In addition to the length of wire needed for hanging, you need 16 inches of wire to secure the wire to the back of the painting. Find the total length of the wire needed to hang the painting. Thanks The home plate, first base and second base form a right angled triangle with two lengths of 65 feet and the hypoteneuse is the distance between home and second base. This means the distance between home and second base is 鈭?65虏 + 65虏) = 鈭?450 鈮?91.9 feet As the pitchers plate is 50 feet from home, it is (91.9 - 50) 41.9 feet from second base ----------------------- As the ladder is 10ft long, the base of the ladder must be at least (10/4) 2.5ft from the wall. To work out how high up the wall the ladder will reach in this case, use pythagoras. We know the hypoteneuse and on of the other sides. 10虏 = 2.5虏 + a虏 100 = 6.25 + a虏 93.75 = a虏 a = 鈭?3.75 a 鈮?9.7ft The ladder will reach approximately 9.7ft up the wall. ----------------------- The length of wire is dependant on how you hang the picture. For example, if you hang it with a piece of wire fastened at two points at the back and the hook between them (forming a triangle) then the length varies depending on how far apart the two attachment points are. The pitcher's plate is 65 feet away from the second base. The minimum distance of the ladder from the wall is 0 feet. The total length of wire needed is (3 feet + 16 inches). |
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