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第6章 物理老师是仲主任?

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着。
    赵胜他们也好奇地探过头去看,因为除了叶安和凌栖月的水平高之外,其他的人水平都是半斤八两,孟含不会的,他们其实也不咋会,能上实验班的人大多数都是比较爱学习的。
    赵胜他们一看,那是一道关于正四棱锥的题目,求侧棱与底面所成角的馀弦值,题目不难,但对于空间想像能力不强的学生来说,确实有点头疼。
    孟含眼珠一转,忽然想到了什麽,抱着练习册就跑到了叶安这一桌。
    「叶大学神,江湖救急!」孟含把本子往叶安面前一推,「这道题除了建坐标系,还有没有别的办法?」
    赵胜和李浩还在那伸着脖子看题,嘴里念叨着:「正四棱锥……侧棱和底面……先找射影……」
    叶安的目光只在题目上扫过一秒。
    【检测到空间向量与立体几何……】
    【逻辑链路推演中……】
    【最优解法已生成:辅助线法……】
    几乎是本能反应,他连草稿纸都没用,直接开口。
    「有。」
    叶安从书包拿起一支笔,在孟含的练习册上轻轻点了几下。
    「你看这个正四棱锥,顶点是P,底面是正方形ABCD,中心是O,要求侧棱PA与底面ABCD所成的角,其实就是求PA和它在底面上的射影AO所成的角,也就是∠PAO。」
    他的声音不疾不徐,思路清晰得可怕。
    「我们不需要建系。连接AC,因为底面是正方形,所以AC等于根号二倍的AB,O是中心,所以AO等于AC的一半,也就是二分之根号二的AB。」
    「这样,在直角三角形PAO中,斜边是侧棱PA,一条直角边是高PO,另一条直角边是AO,角的馀弦值等于邻边比斜边,也就是AO比上PA,题目里肯定给了棱长和高的关系,代入数值就行了。」
    一番话说完,整个桌子都安静了。
    赵胜和李浩张着嘴,还停留在他第一句话的射影上。
    孟含则是眼睛越瞪越大,脸上的表情从迷茫到惊讶,最后化为一片豁然开朗的狂喜。
    「对啊!我怎麽就没想到!直接找角不就行了吗!这麽简单!」她一拍大腿茅塞顿开,「谢谢你叶安!你太厉害了!」
    叶安只是笑了笑,把本子推了回去。
    但凌栖月却停下了吃饭的动作,不知何时已经转过头,静静地看着这边目光落在叶安身上,她清楚地知道,自己早上教给孟含的向量法,是最高效的解法。
    因为所有的几何体的最终方法就是建系,但是建系有个最大的特点就是你往里面代数的时候会出现问题,而且这道题想要建系就要做辅助线证明垂直,相对应的要麻烦很多,叶安给出的直接找角恰好避开这些问题。
    」这家伙还是一如既往的强。」
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