Trapezium

'.' the height of triangle ADC = the height of triangle ADC
( the height of trapezium is common )
'.' DC = DC (common side)
the area of triangle = base x height ÷ 2
'.'triangle ADC and triangle ADC have the same length of base and height
.'. the area of triangle ADC = the area of triangle ADC
LET y be angle MDC
1/2 x 7 DC siny = 1/2 x 5 DC sin( 180° - 120° - y )
7 siny = 5sin(60°-y)
7 siny = 5 ( sin60°cosy - sinycos60°)
7/5siny = (√3)/2 cosy - 1/2 siny
14/5siny = (√3)cosy - siny
19/5siny = (√3)cosy
tany = [5(√3)]/19
y = 24.5° (cor. to 3sig.fig.)
.'. angle MDC = 24.5°

Draw a line // BD from A ,meet CD at N, then AN = BD = 7, AN // BD
So ㄥMDC = ㄥANC , ㄥCAN=ㄥCMD = 120
In △ ANC , by cosine law :
COS 120 = (5^2 + 7^2 - CN^2) / (2*5*7)
CN = √109
In△ ANC , by sine law :
SIN ㄥANC / 5 = SIN 120 / √109
ㄥANC = 24.50 (2 dec.)



2009-06-22 22:57:59 補充：
So ㄥMDC = 24.50° (2 dec.)