F.3 Maths question - triangles

[匿名]

2013-11-23 10:26 pm

Advance F.3 Mathematics question (about triangles) :

Q: In the figure, ABCD is a square of side a and BDP is isosceles. CP // DB. Find the length of the perpendicular BN from B to DP.
圖片參考：http://imgcld.yimg.com/8/n/HA04661785/o/20131123141812.jpg

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回答 (1)

用戶10012

2013-11-24 2:40 am

✔ 最佳答案

By Pythagoras thm., BD = DP = a sqrt 2.
DC = side of square = a.
Since CP//DB, angle PCB = angle DBC = 45 degree.
So angle DCP = 90 + 45 = 135 degree.
By sine rule ( I'm not sure if F.3 should know this),
DP/sin ( angle DCP) = DC/sin (angle DPC)
that is
a sqrt 2/sin 135 = a/ sin ( angle DPC)
sin ( angle DPC) = sin 135/sqrt 2 = ( sqrt 2 / 2)/ sqrt 2 = 1/2
Angle BDP = angle DPC ( since CP//DB)
so sin ( angle BDP) = sin ( angle DPC) = 1/2.
Length of BN = sin ( angle BDP) x BD = (a sqrt 2) /2.

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