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5. 如图，在Rt△ABC中，∠C = 90°，点D在AC上，∠DBC = ∠A.若AC = 4，cosA=$\frac{4}{5}$，则BD的长度为( ).
A.$\frac{9}{4}$ B.$\frac{12}{5}$ C.$\frac{15}{4}$ D.4
A.$\frac{9}{4}$ B.$\frac{12}{5}$ C.$\frac{15}{4}$ D.4
答案
C
6. 在△ABC中，∠C = 90°，AC = 2，BC = 1，则tanA的值是_______.
答案
$\frac{1}{2}$
7. 如图，⊙O的直径AB = 13，弦AC，BD相交于点E，DC//AB，DC = 5，则tan∠AED = _______.
答案
$\frac{12}{5}$
8. 在Rt△ABC中，∠B = 90°，∠A = 30°.以点A为圆心，BC长为半径画弧交AB于点D.分别以点A，D为圆心，AB长为半径画弧，两弧交于点E.连接AE，DE，则∠EAD的余弦值等于_______.
答案
$\frac{\sqrt{3}}{6}$
9. 如图，在△ABC中，AD是BC边上的高，tanB = cos∠DAC.
(1)求证AC = BD.
(2)若cosC=$\frac{5}{13}$，BC = 18，求AD的长.
(1)求证AC = BD.
(2)若cosC=$\frac{5}{13}$，BC = 18，求AD的长.
答案
(1)$\tan B=\frac{AD}{BD}$，$\cos\angle DAC=\frac{AD}{AC}$，
∵$\tan B=\cos\angle DAC$，∴$AC = BD$.
(2)设$DC = 5x$.∵$\cos C=\frac{5}{13}$，
∴$AC = BD = 13x$.∴$BC = 18x = 18$，$x = 1$.
∴$DC = 5$，$AC = 13$.∴$AD = 12$.
∵$\tan B=\cos\angle DAC$，∴$AC = BD$.
(2)设$DC = 5x$.∵$\cos C=\frac{5}{13}$，
∴$AC = BD = 13x$.∴$BC = 18x = 18$，$x = 1$.
∴$DC = 5$，$AC = 13$.∴$AD = 12$.
