如图,已知在三角形AlBC中,点D是BC边上一点,DA垂直于AB,AC=l2,BD=7,CD=9,求证:三角形ACD相似三角形BCA.(2)求tan角CAD的值.
2019-04-10
如图,已知在三角形AlBC中,点D是BC边上一点,DA垂直于AB,AC=l2,BD=7,CD=9,
求证:三角形ACD相似三角形BCA.(2)求tan角CAD的值.
优质解答
证明：△ACD 和 △BCA 中：
∵ AC/BC = 12/16 = 3/4
CD/AC = 9/12 = 3/4
∴ AC/BC = CD/AC
又 ∠C = ∠C
∴ △ACD ∽ △BCA
∴ ∠CAD = ∠B , AD/AB = CD/AC = 3/4
∴ tan∠CAD = tna∠B = AD/AB = 0.75
证明：△ACD 和 △BCA 中：
∵ AC/BC = 12/16 = 3/4
CD/AC = 9/12 = 3/4
∴ AC/BC = CD/AC
又 ∠C = ∠C
∴ △ACD ∽ △BCA
∴ ∠CAD = ∠B , AD/AB = CD/AC = 3/4
∴ tan∠CAD = tna∠B = AD/AB = 0.75