Question 823989
Rule:


Area of Triangle = (Base)*(Height)/2


Note: the base and height are ALWAYS perpendicular segments


Since h is the height (given and fixed), this forces us to choose b as the base since b is perpendicular to h


So....


Area of Triangle = (Base)*(Height)/2


A = b*h/2


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Now focus on the smaller triangle on the left (with hypotenuse 'a' and leg 'h')


sin(angle) = opposite/hypotenuse


sin(theta) = h/a


a*sin(theta) = h


h = a*sin(theta)


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Now go back to the area of a triangle equation and plug h = a*sin(theta) in


A = b*h/2


A = (1/2)*b*h


A = (1/2)*b*(a*sin(theta))


A = (1/2)ab*sin(theta)


So the answer is <font color="red">choice D</font>