1. The area of a parallelogram is 80 cm2. Two of the sides are of lengths 6cm and 15cm. Find the angles of the parallelogram correct to the nearest 0.1度
2. In the figure, ABCD is a rectangle . The diagonals AC and BD meet at E . Let A B=25 , AD = 20 .
a) Mark, on the figure , a point F on BC such that EF垂直BC.
b) Find EF and the actute angle between the diagonals .
急 ~~`中二數學問題(二條)~~要步驟~~求人回答~
2013-08-12 1:25 am
回答 (2)
2013-08-12 2:09 am
✔ 最佳答案
1. height of parallelogram=80/15 =16/3actute angle of the parallelogram =sin-1 ( (16/3)/6 )
=62.7°
obtuse angle of the parallelogram =180°-62.734°
=117.3°
2.
a) F= mid-point of BC
b) EF= half of AB
=25/2
=12.5
∠DAC= tan-1 (25/20)
=51.34°
∴actute angle between the diagonals = 180°-2 (51.34°)
=77.3°
2013-08-12 2:23 am
由於我比 月 答得慢了～
所以我貼在這裏吧～
看圖：
http://imgcld.yimg.com/8/n/HA00430218/o/20130811181607.jpg
2013-08-11 18:23:53 補充：
〔１〕
從上圖設 x cm 為高。
面積 = 15 * x = 80，即x = 16/3。
設綠色的角為 a ，那麼 sin a = x/6 = 8/9
所以計出 a = 62.73395555 度 = 62.7度。
跟住，明顯地對角也是 a, 而另外兩角為 180-62.7 = 117.3 度。
那麼四個角你都知道了。
〔２〕
EF = AB/2 = 12.5
BF = AD/2 = 10
先找出 角BEF 。
tan(角BEF) = BF/EF = 10/12.5
角BEF = 38.65980825 度
題目所求的角為 角BEC = 2*角BEF = 77.31961651 度
所以我貼在這裏吧～
看圖：
http://imgcld.yimg.com/8/n/HA00430218/o/20130811181607.jpg
2013-08-11 18:23:53 補充：
〔１〕
從上圖設 x cm 為高。
面積 = 15 * x = 80，即x = 16/3。
設綠色的角為 a ，那麼 sin a = x/6 = 8/9
所以計出 a = 62.73395555 度 = 62.7度。
跟住，明顯地對角也是 a, 而另外兩角為 180-62.7 = 117.3 度。
那麼四個角你都知道了。
〔２〕
EF = AB/2 = 12.5
BF = AD/2 = 10
先找出 角BEF 。
tan(角BEF) = BF/EF = 10/12.5
角BEF = 38.65980825 度
題目所求的角為 角BEC = 2*角BEF = 77.31961651 度
收錄日期: 2021-04-20 14:08:17
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130811000051KK00188