[从头学数学] 第141节 勾股定理 小结与复习题

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入了筑基中期的修炼，
这次要修炼的目标是[勾股定理 小结与复习题]。

正剧开始：

星历2016年03月19日 14:40:16, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究[勾股定理 小结与复习题]。

<span style="font-size:18px;">	var triangle = new  Triangle();  
    var a = triangle.know2edges([200, 300]);  
    var tmp = [].concat(a);  
	
	config.setSector(2,3,1,1);  
    shape.angleDraw(tmp, 'red', 0.5); 
	
	a = triangle.know2edges([Math.sqrt(7*7-2*2), 2]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,1,2);  
    shape.angleDraw(tmp, 'green', 20); 
	
	a = triangle.know2edges([Math.sqrt(234*234-77*77), 77]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,2,1);  
    shape.angleDraw(tmp, 'orange', 1);

	a = triangle.know2edges([3, 1.5]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,2,2);  
    shape.angleDraw(tmp, 'cyan', 50);
	</span>

<span style="font-size:18px;">function myDraw(xGlobal, yGlobal) {  
	var config = new PlotConfiguration();      
	config.init();  
	
	config.setPreference();  
	var r = 50;
	config.setSector(1,1,1,1);  
	config.graphPaper2D(0, 0, r/2);
	config.axis2D(0, 0,180);  
	
	
	var triangle = new  Triangle();  
    var a = triangle.know2edges([200, 300]);  
    var tmp = [].concat(a);  
	
	config.setSector(2,3,1,1);  
    shape.angleDraw(tmp, 'red', 0.5); 
	
	a = triangle.know2edges([7, 2], -90);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,1,2);  
    shape.angleDraw(tmp, 'green', 20); 
	
	a = triangle.know2edges([234, 77], -90);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,2,1);  
    shape.angleDraw(tmp, 'orange', 1);

	a = triangle.know2edges([3, 1.5]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,2,2);  
    shape.angleDraw(tmp, 'cyan', 50);
	
	
	
	
	/*
	array = triangle.know3edges([13, 14, 15]);

	config.setSector(2,3,1,2); 
	tmp = [].concat(array);
	shape.angleDraw(tmp, 'green', 10);	*/
	
	
	/*
	var mathText = new MathText();
	
	var s = [
		'AE = DB',
		'AD^[2]+DB^[2] = AB^[2]',
		'AB^[2] = AC^[2]+BC^[2] = 2*AC^[2]'
	];
	
	var x =40, y=40;
		var r1 = 40;
		
		var len = s.length;
		for (var i = 0; i < len; i++) {
		
			if (s[i] == '') {
				if (x < 100) {
					x += 300;
					y-=r1*3;
				}
				else {
					x = 20;
					y += r1;
				}
			}
			else {			
				mathText.print(s[i], x, y);
				y+=r1;
			}
		}	*/	
	
}
</span>

进化后的根据两边求三角形元素值：

<span style="font-size:18px;">	//已知2条边和夹角
	this.know2edges = function(edges, angle) {
		this.edges = [];
		this.angles = [];
		
		
		//如果没有指定两边的夹角，默认为90度
		angle = angle ? angle : 90;

		
		var edgeC = 0;

		if (angle == -90) {
			//设定当输入角度为-90时指已知斜边和一条直角边的直角三角形
			var swap;
			if (edges[0] < edges[1]) {
				swap = edges[0];
				edges[0] = edges[1];
				edges[1] = swap;
			}
			edgeC = Math.sqrt(edges[0]*edges[0]-edges[1]*edges[1]);
			angle = Math.asin(edgeC/edges[0]);
		}
		else {
			angle = angle ? angle/180*Math.PI : Math.PI/2;
			edgeC = Math.sqrt(edges[0]*edges[0]+edges[1]*edges[1]-2*edges[0]*edges[1]*Math.cos(angle));
		}
		
		
		this.edges = [edges[0], edges[1], edgeC];
		
		var edgeA = this.edges[0],
			edgeB = this.edges[1];
		
		//角度为弧度单位
		//a边对应角
		this.angles.push(Math.acos((edgeB*edgeB + edgeC*edgeC-edgeA*edgeA)/(2*edgeB*edgeC)));
		
		//b边对应角
		this.angles.push(Math.acos((edgeA*edgeA + edgeC*edgeC-edgeB*edgeB)/(2*edgeA*edgeC)));
		
		//c边对应角
		this.angles.push(angle);	
		
		var x0 = 0, y0 = 0;
		var x1 = x0 + this.edges[0], y1 = y0;
		var x2 = x0 + this.edges[1] * Math.cos(-this.angles[2]),
			y2 = y0 + this.edges[1] * Math.sin(-this.angles[2]);
			
		var retArray = new Array();
		retArray.push([x0, y0]);
		retArray.push([x1, y1]);
		retArray.push([x2, y2]);
		
		return retArray;
	
	}</span>

<span style="font-size:18px;">	//题5
	a = triangle.know3edges([1, 1.732, 2]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,1,1);  
    shape.angleDraw(tmp, 'red', 100); 
	
	//题7
	a = triangle.know2edges([2*1.732+1, 2*1.732-1]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,1,2);  
    shape.angleDraw(tmp, 'green', 50); </span>

<span style="font-size:18px;">	//题9
	a = [[2,0], [0,4], [4,1], [5,5]] 
    tmp = [].concat(a);  
	
	config.setSector(2,3,2,1);  
    shape.angleDraw(tmp, 'red', 30); 
	
	//题10
	a = triangle.know3edges([4.55, 5.45, 3]);  
    tmp = [].concat(a);  
	
	config.setSector(2,3,1,2);  
    shape.angleDraw(tmp, 'green', 50); </span>

本节到此结束，欲知后事如何，请看下回分解。