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電子課本網(wǎng) 第68頁

第68頁

信息發(fā)布者:
C
B
A
0.45
0.45
0.78
0.85
$?\frac {3}{10}\sqrt {10}?$
D
$解:作等腰三角形?ABC,?過頂點(diǎn)?A?作?AD⊥BC,?交?BC?于點(diǎn)?D?$

$①當(dāng)腰長為?6?時(shí),即下圖?AB=6?$
$∵?C_{△ABC}= 20?$
$∴?BC=8?$
$∴?BD=\frac {1}{2}BC= 4?$
$?cos B =\frac {BD}{AB}=\frac {2}{3}?$
$②當(dāng)?shù)走呴L為?6?時(shí),即圖中?BC=6?$
$∵?C_{△ABC}= 20?$
$∴?AB=7?$
$∴?BD=\frac {1}{2}BC= 3?$
$?cos B=\frac {BD}{AB}=\frac {3}{7}?$
$綜上所述,底角的余弦為?\frac {2}{3}?或?\frac {3}{7}?$
$解:過點(diǎn)?D?作?DE⊥BC,?垂足為?E?$
$∵? ∠A=∠ABC=90°?$
$∴? AD//BC?$
$∴? ∠ADB=∠CBD?$
$∵? DB?平分?∠ADC?$
$∴? ∠ADB=∠CDB?$
$\ ∴? ∠CDB=∠CBD?$
$∴? CD=BC=3?$
$∵? AD=BE=1?$
$∴? CE=BC-BE=2?$
$在?Rt△CDE?中,?DE=\sqrt 5,??BD=\sqrt{6}?$
$∴? sin ∠ABD=\frac {AD}{BD}=\frac {\sqrt{6}}{6}$