公务员考试网 发表于 2017-4-6 09:51:02

数量关系答题技巧之生活中的几何问题

近年来,考查与实际生活相关联的内容是几何问题这类题型的一种新的命题趋势。纵观这几年国考、联考试卷中考到的几何问题,会发现,题目内容都很生活化,但考点并不生活,反而跟初高中数学的几何密切相关,有以下三点:
一:三角函数,主要考查最基本的sin,cos,tan;
二:两点间线段最短;
三:三视图。
例题1、一艘轮船在海上由C点向正北方向的D点匀速行驶,出发时看见正西方有两座灯塔与该船在同一直线上,两个灯塔(A塔和B塔)之间相隔10海里。航行30分钟后到达D点,看见其中一座灯塔(B)在南偏西60°方向上,另一灯塔(A)在南偏西75°方向上,求船速( )
http://www.zzxingce.com/xingce/datijiqiao/shuliangguanxi/20140210/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAB/CAIAAAAckqtfAAAQ2UlEQVR4nO3dfzRU+f8H8JffIolk6ZeYijrZsJXKdmoTqlW0yGL7tZ9O64gom1qrWjroh2ps2hynH7bMyRL6sRXb0pbSKQzVarGzSj8IJT8GoZn7/ePdd9aKa8zcO3fMvB+nv+55z72vtufeO3Pfv4DAMEYB0wVgyu59BPnv/v3T+o7oEDBbFSZ3iouL80ndunVL1Ljt3X8S1d8fBEcQG1hSUhKIYe3atV2dnQSOIEY5BwcHFov1kNTGjRsBoI3PJ3AEMco5OTnNmDGDvE1UVJS6unp7WxuBI4hRztnZ2dramrxNRESEhoYGjiBGi14RLCkpSUlJqays7NkGRxCjUa8Ienp6hoaGhoWFPXz4UHQQRxCjUa8Irl+/vqam5uXLl+vWrXv9+jU6iCOI0ejDCJaVlREE4erqWltbiw7iCGI06hXBVatWXb9+/fjx40lJSW/fvkUHcQQxGvWK4N69e318fJKSknq2wRHEaIRfymAMc3JysrW1JW8TExOjpqaGI4jRYsWKFaampmxSjo6O2traOIIYLVauXDngGAV1dXUrK6v29nYCRxCjUGFh4XfffaelpTVv3rx6Ug0NDa9fvxYKhQSOIEaVK1eu6OnpoZuco6Oj+B/EEcSk0t3dXVpaam9vr6KiAgCampr6+vrz588X/ww4gpjkzp075+npCQDGxsYzZ84EgIyMDE9PzwFfyvSEI4hJoqCgwMXFBQBUVFTi4uI4HI6lpeXhw4cJgnBxccERxGjU2NiYlZWlr6+vq6vr5+fH5/MrKirMzMxGjRqFuoDFeTXdE44gNggHDhxAD9zx48c/ePCAIIj79++bmJiMGTOmtLQUtcERxKhXX1+fmpo6efJkADA1NU1KSnr69ClBEIWFhcOHDzcwMEBxRHAEMYrxeDxLS0sAmDJlys6dO9HLPIIguFzu6NGjTUxMuFxuz/Y4ghhlWlpa/P39jY2NtbW1k5OTRaP9CIK4c+eOoaGhqanpo0ePen0KRxCjwJ9//hkbG6utrQ0Ac+fOzc3N7dXAwMDAwMBA9P2vJxxBTCr19fUhISHDhw8HgCVLliQnJ3/Yhs1mjxw5stfzVwRHEJNcRUXF3LlzAWD69On5+fkdHR0ftjly5AgArFmzpr+T4AhiksjOzt6wYQPq4U1PT++vWUJCAgA4OTnx+fz+2uAIYoMgFAofPHiwbNkyFL6AgIA//vijv8aJiYkAsGLFitbWVpJz4ghi4mpvb0c9vGpqasuXL3/y5AlJYzabDQCurq6dnZ3kp8URxMSSmJi4cOFCAAgODr5z5w55459++gkAXFxc2traBjwzjiBG5s2bN5cvX542bRoAjBo1Ki4ubsCPnD9/HgDc3NxIvv/1hCOI9evEiROzZs0CgLFjxwYHB/f5g7eXzs5OV1fXhQsXitMYwRHE+sDn8wMCAtCkjaNHj1ZVVYn5QW9vbwAY8EndE44g9h88Hu/o0aNoSH14eHjPTjZynZ2dfn5+ALBv3z7RKgjiwBHE3mttbd2+fbuJiQkAzJkzJyEhQfzPdnd3e3h4AEBMTMxgr4sjiBEEQURHR48ZMwYAzMzMcnJympqaxP9sV1eXr68vAERHR0twaRxBZZefn79lyxYAWLBgwfHjx9+9ezfwZ3p4+/Ytell44MAByQrAEVReVVVVK1euRDPZ/Pz8BAJJ/mG+/PJLie9/CI6gMiooKNiwYQMK38KFC//66y/J8sfj8TQ1NaXJH4EjqIROnTqFeni//vrr7Oxsic9TUVExfvz4iRMnSlkPjqCyaGtru3XrlrW1NQA4OzvfvXtXmrPxeLxx48apq6t/ODp1sHAElQKHw3F0dAQAfX39DRs2tLS0SHO2ysrKyZMn6+rq5uXlSV8bjqCCu3jxIppDDgCxsbE9l7GXTHl5+YQJE4YNG3bz5k1KKsQRVFgvXrxISUlBwws2bdr04sUL6c/5+PFjc3NzbW1tSu5/CI6gAhIIBJGRkWga74wZM9AcXumVl5dbWFjo6en13BdTejiCCqWmpiYhIYHFYgHARx99lJ6eXldXR9XJ9+7dq6OjQzJMWjI4goqDy+UaGxsDgJ2dXVxcXHd3N4UnT09PB4Aff/yRwnMiOIKKoK6uzs/PT0dHZ9y4cRwOR8yxouJLTU0FAAcHh+rqamrPTOAIDnXFxcWhoaFaWloAMHv27J5rtVCFw+EAwKxZs0TbcVELR3CoqqysDAsLQ29bvLy8zp07R8dVMjIyAMDe3p7C75S94AgOPV1dXaWlpRMnTgSATz/9tKCggKYLoXc6Dg4ONN3/EBzBISYrKwsNDtXR0fn9998lG14gjrNnzwKAjY1NQ0MDTZdAcASHBoFAcPPmzRUrVqAnb3h4uJSdvAMyMzObOXNmfX09rVchcASHhFevXqE5vLq6ul999RVVr5pJ+Pv7q6io0H3/Q3AE5d3Bgwft7OwAICwsDG3USzc0dy44OFgG1yJwBOXWq1evOBwOmkNuaGh49uxZ2Vw3JCQEALZu3SqbyxE4gnKoo6MjOTkZdbJZWVnt2rVrwGVZqLJx40YA+Pbbb2VzOQRHUL6w2Wy0RL2hoeGJEydk8GtAJDAwEACCgoJkdkUER1BelJWV7dmzBwBYLBabzX758qXMLt3S0hIUFAQAO3bskNlFRXAEmVdTUxMeHq6jowMAHh4eXV1dMi4gPz9fxt//esIRZNKzZ8+2bNkyevRoALC2tr5x48aglsKgRENDg5WVlbe3t4yvK4IjyJgzZ86g98zOzs4ZGRmyv/kRBFFbW2tvbw8AV69elf3VERxBBpSUlHh5eaEFDDgcDlNl1NbWTp8+HQCysrKYqoHAEZSxgoICd3d3AFBVVXV1dSVfhJlWDQ0N6Kd3WloaUzUgOIIykpubK1qiPjAwkO4eXnIvXrz45JNPVFRULl26xGAZCI4g7Zqbmy9duqSurq6qqrp27dpBLf9Ih+fPn9vY2KDtqJmtBMERpFdKSoqtrS1621dZWcl0OQRBEGisV2ZmJtOFvIcjSIvu7u7k5OQFCxYAgJaWVkJCAvkWCTJz9epVHR2d1NRUpgv5F44g9UpLSy0sLABg3LhxP/zww7Nnz5iu6L1r164BgIWFxWAXEaQVjiCVmpubd+/ePXr0aCMjox07djQ3NzNd0b/y8vKGDRtmaWnJ4/GYruU/cASpUVNTExUVZWZmBgDm5uZ97nrKoJycHA0NjSlTpsjPLVkER1Ba1dXVx44dQ1vxOjg4nDx5UvadbOTy8vI0NDQsLCz++ecfpmvpA46gVHg8Hlq6xcbG5uTJk0yX05tQKMzOztbW1p42bdrjx4+ZLqdvOIISKiwsXLdunbq6upqa2sWLF9+8ecN0RX2or69XVVU1NzeXk9/jfcIRHLS7d++iJeoBYN26ddeuXWO6on5t37590qRJf//9N9OFkMERHITW1lY3Nzc1NTW0ze6NGzeYrohMdHQ0AERGRjJdyABwBMWVlpaGZlK6u7tzuVz65pBTYufOnQCwevVqRsaADQqO4AAEAkFmZqZoH/Kff/6Z6YoGhiYA+Pr6Uru+G01wBPvV2dl5+/btGTNmoMlEwcHBcvujsqddu3YBwPr16+WqC4QEjmDfurq6Vq5ciZZuCQsLo2ShZhnYvXs3uv8JhUKmaxEXjmBvDQ0N8fHxlpaWABAVFUXHin00SUhIQPe/IfH8FcER/FdDQ8Pp06eNjIwAwNbW9vDhw0xXNAhNTU12dnZeXl5MFzJoOILvRUZGotUzLCwskpKS2tvbma5oEFpbW9HAsOfPnzNdy6DhCBIPHjxAr5qnTJly5swZWS5gQInW1talS5cCwLFjx+T/FcyHlDqCjx49Cg8PR29bNm/ezHQ5kmhqalq0aBEAyGEPtZiUNIK1tbVr1qzR09NDMyml38uPER0dHYsXL0b3P6ZrkZwyRjA2Nhbd+ZYtW3b9+vWh9ftRpKmpacmSJQBw4sQJpmuRinJFMDc3F03ecXd3p2mJetno6uqaP38+ABw/fpzpWqSlLBEsLCxE/2a6urpr166V2Yp9NLl16xYAHD16lOlCKKD4EczMzPTx8UFP3pCQEDmZSSmN4uLiESNGODk5MV0INRQ5gm/evDl16hQAqKurh4aGFhYWyujCdLp3797IkSONjY25XC7TtVBDMSPI5/PT09PR5jDz5s2T5XKRtLp//76RkZGRkVFRURHTtVBG0SIoFAoPHTo0e/ZsADAyMjp27BitOwfJ0r1794yMjExNTYdQt7U4FCqCOTk5Y8eOBYCJEyceOXJEDicsSqyoqEhPT09fX1/epodKT0Ei+PTp05iYGC0tLRaLFRERMVSGyonp3r17xsbGpqamCvP9r6chH8G6urqgoCC0FbSNjc1Q7Kcf0DfffDNixAjZ7Hsje0M4gmVlZfv371dVVQWARYsWXbhwoaOjg5pTyxM0CvDXX39luhC6DNUIFhYWTpgwAQDc3NzkZ50yyiUlJampqXl5ecnbCg0UWrp06fTp08Vvz3AE+Xw+l8t1c3MzMDAAADabnZ+f/+TJk5KSEq7CiY+PR+MXb9++/fDhQ6bLocucOXNsbGyGTARRxxSmYOzt7ZmPYEtLSz0ptDFpS0tLdnb2b/8vW6Hl5OQow1/zt99+G9SbdloiWFZWZm1tPeD/K9u2bRvqwwsw6dESQX9/fwA4fPgwu3++vr4AIJ/Lk2GyREsEAwMDR4wYQX7hrKwsABgSk8klU1BQwGKxDPtnamoaHx+PnwO0RDAoKEhPT4+8S+P06dOKHUErK6uxY8f69w/NkVPI50BiYmI0qX379on6+mUXwV4LNSt8BM3MzHx9fUkaXLhwAQCqqqpkVpJsoBUgBvTZZ5+hl6MyiuD58+e3bNnSM3AKH0ELCwsPDw+SBikpKQoZwfnz50+dOrWZ1LZt2wCgjc8nZBNBgUAQEBAQExNz5MgR0dooyhZBoVDI5/P5fL7oiKJG0NnZ+eOPPyZvs3v3bg0Njfa2NkI2ETx48OD27dvPnj37xRdfiHYoULYIrlmzxsvLy8fHp7i4GB1R4AgO2EccEREh0wiGhIR8/vnnW7dunTRpkmiqh1JFUCgUuru7NzY2NjY2enp6okeB8kQwPj4+MjKytrZWdESmEbx7925kZCQa81JUVLRnzx7URqkiSBDE4sWLvb29V61atWjRInRESSK4f//+uLi4lJSUnTt3in6SyjSCbW1tPcdciX6KK1UEhUKhh4dHdXV1dXX1kiVLlOou6O3tjb59NTU1iR6M0kawUzhwBAd8NZ2WlqY8ESQIwsnJyd/fPzAwULRloZJE0NfXt6KiolcbaSNY3fqujTSCmzdv1tHRKSkpud8/tH688kSQx+PdvHkzPz9fdERJIvj999+fPHkyNzc3MjKyqakJHZQ2ggeL2giC6CL6jWBISIiYo3oU7x9AxNzcnHyBytTUVIX8L9ArggKBICIiYtOmTeXl5aJXctJGMCS1uJLH+6uupfUdwe8rguXl5VeuXPmV1OXLl7Ozs4fWypODwmKxli9f/rp/iYmJyhDBPkkbQU/f1T5frQ7m3G4UEu0C5lfWkk8sFkuc54Ccb6UkAScnJ1tbW/I2MTExampqkkewiyAEBNHd/4MYIwjil19+YbPZcf07dOhQQkKCXO1xTAkXFxctLa31pKZOnaqpqdkucQfd//zzGgnirQBHEOtDaGiolZXVR6TMzc0dHR3R2zpJInguNuM5QXT0/4sYw8QnSQQvsy/gCGJUkSSCGMYUHEGMYf8Hw3BVWRneGrQAAAAASUVORK5CYII=
A 、5海里/小时
B 、8海里/小时
C 、10海里/小时
D 、12海里/小时
解析:本题考查了解直角三角形的应用,解题的关键是对方向角的掌握和正确的运用.要求速度,需找DC的距离。根据题意得:∠ADC=75°,∠BDC=60°,DC⊥AC,∴∠DBC=30°,∠BDA=∠A=15°,∴BD=AB=10,∵DC⊥AC,∴在Rt△BDC中,

        [*]
                ×sin∠DBC=10×(1/2)=5,∵从C到D行驶了半小时,∴速度=5÷0.5=10海里/小时。故答案为C。

例题2、某公司要在长、宽、高分别为50米、40米、30米的长方体建筑的表面架设专用电路管道联接建筑物内最远两点,预设的最短管道长度介于( )?
A 、70—80米之间
B 、60—70米之间
C 、90—100米之间
D 、80—90米之间
解析:根据题干我们可得一个长、宽、高分别为50米、40米、30米的长方体,设其上面四个顶点为A、B、C、D,下面四个顶点为A1、B1、C1、D1。故最远的两点应为A1C。要使表面铺设的管道长最短,需要先将平面ABA1B1和平面ABCD拉伸,组成一个平面,那么要得到A1与C的最短距离,即它们的连线,其长度为:根号下[(BC+B1B)^2+A1B1^2],即:根号下[(30+40)^2+50^2]。故答案为D。
例题3、若干个相同的立方体摆在一起,前、后、左、右的视图都如图,问这堆立方体最少有多少个()?
http://www.zzxingce.com/xingce/datijiqiao/shuliangguanxi/20140210/data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAA1CAIAAACP7yF2AAAAmklEQVRoge3XOw7DIBBAQe5/I+6VMhJpUlhBkYPNLzBP21jaYscdIe1UGH1A197ax3Px+dT+V7S0tLRzR9tLG8q7hx2tbbqfR0tLS1sSbc39PFpaWtqSaGvu59HS/qK98F7tUENt0Z9uvZ9SijEeP2lpaWlbXk97Ei0tLW3H62lPoqW9pp0w2hra+aOl/aZde2jXnY21m7SX9gVFL8WxvO2vHwAAAABJRU5ErkJggg==
A、4
B、6
C、8
D、10
解析:本题考查的正是几何问题中的三视图。要行程如图所示的视图,又要时立方体数量最少,应该是让三个正方体棱与棱相连(第一个与第二个,第二个与第三个)呈斜线摆设(想象一下楼梯的阶梯变成正方体,然后横放下来,就是所说的斜线摆设),中间的正方体上方再堆一个视图就可以满足题意。考生应注意视图是将物体按正投影法向投影面投射时所得到的投影。故答案为A。
       
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