6.9 项目:基本三角测量
Section outline
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Baseball has often been called America's national pastime. The game is played on a field that consists of four bases. These four bases create the corners of a large square that is called the baseball diamond. Each side of the diamond has a length of 94 feet. Right triangle trigonometry can be used to determine how far a ball must be thrown between bases. The Law of Cosines and Law of Sines can also be used to determine how far a ball must be thrown, and how far a baseball player needs to run from other locations on the field.
::棒球通常被称为美国的国家消遣。 球场由四个基点组成。 这四个基点创造了一个大广场的角, 也就是棒球钻石。 钻石的每边都有94英尺长。 右三角测量法可以用来确定球在基点之间必须投出多远。 科辛斯法则和辛那斯法则也可以用来确定球投出多远,棒球运动员需要从球场上其他地点跑多远。- If the baseball player standing at 3rd base has the ball and wants to throw it to the 1st baseman, what is the shortest distance the ball can travel from 3rd base to 1st base?
::如果站在三垒的棒球选手 拿到球,想扔到第一垒手 球能从三垒跑到第一垒的距离是多少?
- If the catcher is attempting to throw out a runner trying to steal 2nd base, how far would the catcher need to throw the ball if he stands 3 feet behind home plate?
::如果捕手想把一个跑者扔出去 试图偷二垒 如果捕手站在家盘后面三英尺处 投球需要多远?
- A standard pitcher's mound is 60 feet and 6 inches from home plate. Break the diamond into four triangles using the pitcher's mound as one of the vertices of each triangle. Determine if the pitcher's mound is precisely in the middle of the baseball diamond by calculating the distance from all the bases.
::标准投手投手的投手丘体距本垒板60英尺6英寸。 用投手的投手丘作为每个三角形的顶峰之一,将钻石打成四个三角形。 确定投手的投手丘体是否正处在棒球柱的中间, 计算出与所有基地的距离 。
- During a baseball game, an outfielder catches a ball hit to dead center field, 400 feet from home plate. How far does the outfielder have to throw the ball to get it to 1st base?
::在一场棒球比赛中，一名外野手在中外野接住了一个球，该位置距离本垒板 400 英尺。这位外野手需要将球投出多远才能传到一垒？
- During a televised baseball game, the outfielder in center field is playing approximately 330 feet from the television camera that is behind home plate. A batter hits a fly ball that goes to the wall, 420 feet from the camera. How far does the center fielder need to run to make the catch if the camera turns 8° to follow the play?
::在电视播放的棒球比赛中,中场的场外野战手正在离离家盘后面的电视摄像机大约330英尺处玩耍。 击打者击中了飞向墙壁的飞球,距离摄影机420英尺处。 如果摄影机转8度,摄像头要跑多远才能赶上球?
- If the baseball player standing at 3rd base has the ball and wants to throw it to the 1st baseman, what is the shortest distance the ball can travel from 3rd base to 1st base?
