在三角形ABC中，角C=90度。
\u5728\u4e09\u89d2\u5f62ABC\u4e2d\uff0c\u89d2C=90\u00b0\uff0c\u89d2A=15\u00b0\uff0cAB=12\uff0c\u5219\u4e09\u89d2\u5f62ABC\u7684\u9762\u79ef\u662f\u89e3\uff1a\u4f9d\u7167\u9898\u610f\u505a\u56fe\uff0c\u76f4\u89d2\u4e09\u89d2\u5f62ABC\u4e2d\uff0c\u89d2ACB\u4e3a90\u5ea6\uff0c\u89d2BAC\u4e3a15\u5ea6\uff0c\u659c\u8fb9AB=12\uff0c\u4ee5B\u4e3a\u9876\u70b9\uff0cBC\u4e3a\u89d2\u7684\u4e00\u8fb9\u505a\u89d2CBD=60\u5ea6\u4ea4\u7ebf\u6bb5AC\u4e8eD\u70b9\uff0c\u5219\u4f9d\u9898\u610f\u77e5\u89d2DBA\u7b49\u4e8e15\u5ea6\u7b49\u4e8e\u89d2CAB \u8bbeBC\u7b49\u4e8eX\u5219\u6709BD=BC/sin30*=2x,CD=BC*tan60*=\u6839\u53f7\u4e09\u500dx\u53c8\u7531DBA\u7b49\u4e8e15\u5ea6\u7b49\u4e8e\u89d2CAB\u77e5AD=DB=2X\uff0c\u6240\u4ee5AC=\uff082+\u6839\u53f7\u4e09\uff09x\uff0c\u6240\u4ee5 AB2=\uff08\uff082+\u6839\u53f7\u4e09\uff09\u7684\u5e73\u65b9+1\uff09X2=12*12=144 \u800c\u4e09\u89d2\u5f62\u9762\u79ef\u7b49\u4e8e\uff082+\u6839\u53f7\u4e09\uff09X2/2 \u8054\u7acb\u4e8c\u5f0f\u5b50\u89e3\u5f97X2=36\uff082-\u6839\u53f7\u4e09\uff09\u6240\u4ee5\u9762\u79ef\u7b49\u4e8e36\uff082-\u6839\u53f7\u4e09\uff09\uff082+\u6839\u53f7\u4e09\uff09/2=36/2=18 \u8fd9\u662f\u521d\u4e2d\u7684\u505a\u6cd5\uff0c\u901a\u8fc7\u51e0\u4f55\u53d8\u6362\uff0c\u5c0615\u5ea6\u89d2\u8f6c\u6362\u621030\u5ea6\u89d2\u8fdb\u884c\u8ba1\u7b97\u4e5f\u53ef\u4ee5\u7528\u9ad8\u4e2d\u7684\u505a\u6cd5\uff0c\u901a\u8fc7\u4e09\u89d2\u51fd\u6570\u7684\u5173\u7cfb\u6709 \u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u90a3\u4e48AC=ABcos15 S(ABC)=1/2*AB*AC*sin15=1/2*AB^2*sin15*cos15=1/4*AB^2*sin30 =1/8*AB^2=1/8*144=18
\u89e3\uff1a\uff081\uff09\u2235\u2220A=60\u00b0\uff0c\u2220B=90\u00b0-\u2220A=30\u00b0\u4e14b=4
\u2234c=2b=8
\u2235a²\ufe62b²\uff1dc²
\u2234a\uff1d4\u221a5 (\u221a\u4ee3\u8868\u6839\u53f7\u4e0b\u540c\uff0c\u6211\u6253\u4e0d\u51fa\u6765\u6839\u53f7)
\uff082\uff09\u2235a²\ufe62b²\uff1dc²\u2234b\uff1d1\uff0f3=a\u2234\u4e09\u89d2\u5f62ABC\u662f\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u2234\u2220A\uff1d\u2220B=45\u00b0
(3)\u2235\u2220B=30\u00b0\u2234\u2220A=60\u00b0\uff0c2b=c=28\u221a2
\u53c8 \u2235c=28\u221a2\u4e14a²\ufe62b²\uff1dc² \u2234a=14\u221a6
(1)a^2+b^2=c^2，那么b^2=c^2-a^2=289-64=225，所以b=15 cm
(2)a^2+b^2=c^2，那么a^2=c^2-b^2=525-576=49，所以a=7 cm
根据勾股定理 c^2=a^2+b^2
(1) 17^2-8^2=225 开根号为15
(2) 25^2-24^2=49 开根号为7
1）b=15
2)a=7
(1)15cm
(2)7cm
绛旓細璇佹槑锛氬垎鍒欢闀緽E銆丄C鐩镐氦浜嶧锛屸埖AE骞冲垎鈭燘AC锛屸埓鈭燛AB=鈭燛AF锛屸埖AE鈯E锛屸埓鈭燘EA=鈭燗EF=90掳锛屸埖AE=AE锛屸埓螖AEB鈮屛擜EF锛屸埓BE=EF锛屸埓BF=2BE銆傗埖鈭燗CB=鈭燘CF=90掳锛屸埓鈭燙AD+鈭燜=鈭燙BF+鈭燜=90掳锛屸埓鈭燙AD=鈭燙BF锛屽湪螖ACD涓幬擝CF涓紝鈭燙AD=鈭燙BF锛屸垹ACD=鈭燘CF=90掳锛孉C=BC锛屸埓...
绛旓細鍦ㄤ笁瑙掑舰ABC涓紝瑙扖=90搴锛岃A銆佽B銆佽C鎵瀵圭殑杈瑰垎鍒负a銆乥銆乧锛岃嫢a:b=2:3,c=2鏍瑰彿13,鍒檃=___b=___锛熺敱浜嶤=90掳 鎵浠ワ紝a^2+b^2=c^2=52 鍙堢敱浜巃/b=2/3 涓や釜寮忓瓙鍙互寰楀埌a=4 b=6
绛旓細鈭礏D骞冲垎鈭ABC 鈭粹垹CBD=鈭燗BD=30掳 鈭礑E鈯B 鈭粹垹BED=鈭C=90掳 鈭礏D=BD 鈭粹柍BCD鈮屸柍BED 鈭碆E=BC=1/2AB (1)銆佺浉绛夌殑瑙掓湁锛氣垹AED=鈭燘ED=鈭燙锛屸垹CBD=鈭燚BE=鈭燗锛屸垹ADE=鈭燘DE=鈭燘DC=鈭燗BC(鍙湪鍏朵腑浠婚変笁瀵)(2)銆佺浉绛夌殑绾挎鏈夛細AE=BE=BC锛孉D=BD锛孌C=DE (3)銆佸叏绛涓夎褰鏈夛細...
绛旓細涓嶇瓑寮忕粍x+124鈮+62x+23锛瀤-3鐨勮В涓猴細-4鈮锛11 鈥︼紙4鍒嗭級鎵浠=10锛 鈥︼紙5鍒嗭級锛2锛夊鍥撅紝璁綜E=x锛屽垯BE=8-x锛庘埖AE骞冲垎鈻ABC鐨勫懆闀 鈭6+x=10+锛8-x锛夆埓x=6 鈥︼紙7鍒嗭級鈭碈E=6锛孊E=2锛屽張鈭礎C=6锛屸垹C=90掳锛屸埓鈻矨CE涓虹瓑鑵扮洿瑙涓夎褰 鈭粹垹AEC=45掳 鈥︼紙8...
绛旓細锛1锛夆埖鈭燗=30掳锛屸垹C=90掳,鈭碆C=1/2AB=c/2锛孉C=鈭氾紙AB²-BC²锛=鈭3/2c.锛2锛夆埖鈭燙=90掳锛屸垹A=45掳锛屸埓AC=BC=鈭2/2AB=鈭2/2c.
绛旓細濡傚浘锛屽湪鈻ABC涓紝鈭C=90掳锛孉C=4锛孊C=2锛岀偣A锛孋鍒嗗埆鍦╔杞村拰Y杞翠笂锛屽綋鐐笰鍦╔杞翠笂杩愬姩鏃讹紝鐐笴闅忎箣鍦╕杞翠笂杩愬姩锛屽湪杩愬姩杩囩▼涓紝鐐笲鍒板師鐐圭殑鏈澶ц窛绂绘槸锛熻В锛氳鈭燗CO=伪锛屽垯鈭燘OC=90掳+伪 鍦ㄢ娍BOC涓敱浣欏鸡瀹氱悊寰桹B2=BC骞虫柟+OC骞虫柟-2BC OC cos(90掳+伪)鈭礎C=4,BC=2 鈭碠C=AC ...
绛旓細AC=BC 瑙扖绛変簬90搴 DE鍨傜洿AB 鎵浠ユ槸涓夎褰BC. BDE绛夎叞鐩磋涓夎褰 DE=BE DB=鈭2DE DE+BE+DB=4 閭ｄ箞锛2+鈭2锛塂E= DE=2(2-鈭2)AD骞冲垎瑙扖AB AD=AED 瑙扖=瑙扐ED 鎵浠モ柍ACD鍏ㄧ瓑浜庘柍AED 閭ｄ箞CD=DE=BE 鎵浠B=DB+DC=DB+BE=2鈭2 AB=鈭2CB=4 ...
绛旓細瑙ｏ細锛1锛夊湪Rt鈻矨DE涓紝鐢盇E=6锛宑osA= AE/AD= 3/5锛屽緱锛欰D=10锛岀敱鍕捐偂瀹氱悊寰桪E=鏍瑰彿锛 AD鐨勫钩鏂-AE鐨勫钩鏂)= 鏍瑰彿(10鐨勫钩鏂-6鐨勫钩鏂)=8 鈭礏D骞冲垎鈭ABC锛孌E鈯B锛屸垹C=90掳锛岃骞冲垎绾挎ц川寰楋細DC=DE=8锛庯紙2锛夋柟娉曚竴锛氱敱锛1锛堿D=10锛孌C=8锛屽緱锛欰C=AD+DC=18锛庡湪鈻矨DE涓庘柍ABC锛...
绛旓細璇佹槑锛氬洜涓 鍦ㄤ笁瑙掑舰ABC涓紝瑙扖=90搴锛屾墍浠 瑙払+瑙払AC=90搴︼紝鍥犱负 瑙扖FD+瑙払AC=90搴︼紝鎵浠 瑙払=瑙扖FD 鍥犱负 DE鍨傜洿浜嶢B锛孍涓哄瀭瓒筹紝瑙扖=90搴︼紝鎵浠 瑙払ED=瑙扖=90搴︼紝鍙堝洜涓 BE=CF锛屾墍浠 涓夎褰DE鍏ㄧ瓑浜庝笁瑙掑舰FDC锛堣锛岃竟锛岃锛夋墍浠 DE=DC锛屽洜涓 瑙扖=9...
绛旓細鈭碘垹C=90掳锛屸埓鈭燙AB+鈭燙BA=90掳锛屸埓鈭燛AB+鈭燗BF=270掳锛屸埖AD銆丅D鍒嗗埆骞冲垎鈭燛AB銆佲垹ABF锛屸埓鈭燚AB+鈭燚BA=1/2(鈭燛AB+鈭燗BF)=135掳锛屸埓鈭燚=180掳-(鈭燚AB+鈭燚BA)=45掳銆
