Question 1135553
{{{drawing(400,2400/7,-1,6,-1,5,green(line(.5,0,.5,3sqrt(7)/2)),

locate(3,2,"a=?"),
locate(0,0,A),locate(5,0,C), locate(.49,4.3,B), green(locate(.6,2,h)),
locate(.5,0,D), locate(1.6,-.3,AC=b=5),locate(-.9,2,AB=c=4),
triangle(0,0,5,0,.5,3sqrt(7)/2) )}}}{{{matrix(10,1,
matrix(1,3,Draw,height,h),
matrix(1,3,area,""="",expr(1/2)*base*height),
matrix(1,3,15sqrt(7)/4,""="",expr(1/2)*AC*BD),
matrix(1,3,15sqrt(7)/4,""="",expr(1/2)*b*h),
matrix(1,3,15sqrt(7)/4,""="",expr(1/2)*5*h),
matrix(1,4,Multiply,through,by, 4),
matrix(1,3,15sqrt(7),""="",2*5*h),
matrix(1,5,Divide,both,sides,by,5),
matrix(1,3,3sqrt(7),""="",2h),
matrix(1,3,3sqrt(7)/2,""="",h) )}}}{{{matrix(10,1,

matrix(1,3,Use, Pythagorean,theorem),
matrix(1,3,AD^2+BD^2,""="",AB^2),
matrix(1,3,AD^2,""="",AB^2-BD^2),
matrix(1,3,AD^2,""="",c^2-h^2),
matrix(1,3,AD^2,""="",4^2-(3*sqrt(7)/2)^2),
matrix(1,3,AD^2,""="",16-(9*7)/4),
matrix(1,3,AD^2,""="",64/4-63/4),
matrix(1,3,AD^2,""="",1/4),
matrix(1,3,sqrt(AD^2),""="",sqrt(1/4)),
matrix(1,3,AD,""="",1/2))}}}{{{matrix(6,1,

matrix(1,3,AD+DC,""="",AC),
matrix(1,3,1/2+DC,""="",b),
matrix(1,3,1/2+DC,""="",5),
matrix(1,3,DC,""="",5-1/2),
matrix(1,3,DC,""="",10/2-1/2),
matrix(1,3,DC,""="",9/2) )}}}

{{{matrix(10,1,

matrix(1,3,Use, Pythagorean,theorem),
matrix(1,3,BC^2,""="",DC^2+BD^2),
matrix(1,3,a^2,""="",DC^2+h^2),
matrix(1,3,a^2,""="",(9/2)^2+(3*sqrt(7)/2)^2),
matrix(1,3,a^2,""="",81/4+(9*7)/4),
matrix(1,3,a^2,""="",81/4+63/4),
matrix(1,3,a^2,""="",144/4),
matrix(1,3,a^2,""="",36),
matrix(1,3,sqrt(a^2),""="",sqrt(36)),
matrix(1,3,a,""="",6))}}}{{{matrix(8,1,
matrix(1,3,BD/AB,""="",sin(A)),
matrix(1,3,h/c,""="",sin(A)),
matrix(1,3,(3sqrt(7)/2)/4,""="",sin(A)),
matrix(1,3,expr( (3sqrt(7))/2 )*expr(1/4),""="",sin(A)),
matrix(1,3,(3sqrt(7))/8,""="",sin(A)),
matrix(1,3,0.9921567416,""="",sin(A)),
matrix(1,5,Use,inverse,sine,on,calculator),
matrix(1,3,82.8,""="",A)  )}}}

Edwin</pre>