有題F.5 MATHS唔識..(已解決 thx)

imsd

In the figue,ABC is a sector with centre at B
and CDFG is arectangle.DF intersect arcAC at E.
CD=4,CG=5 and GB=3.
Find the area of the shaded region correct  to 3 sig.fig.

09-4-20 09:19 PM 上傳

下載附件 (10.54 KB)

A. 1.25
B. 1.28
C. 1.34
D. 1.39(ANS)

[ 本帖最後由 imsd 於 2009-4-21 05:58 PM 編輯 ]

Naozumi

From triangle BXE, BX = sqrt(8^2 - 4^2) = 4 sqrt(3)
so DE = XC = 8 - 4sqrt(3)

Also, From triangle BXE, it is easy to find that sin EBX = 4/8 = 1/2, so angle EBX = 30 degrees

Area of shaded region = area of trapezium DEBC - area of sector EBC