Question 1210136
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Answer: <font color=red>1536 square units</font> 


Explanation
tangent is the ratio of opposite over adjacent
tan(theta) = 3/4
tan(theta) = opposite/adjacent
opposite/adjacent = 3/4
If we didn't know anything about the hypotenuse, then we could have a 3-4-5 right triangle. Or we might have a 6-8-10 right triangle. 
In general we have a 3x-4x-5x right triangle for some positive real number x.


The hypotenuse is given to be 80 units long, so,
5x = 80
x = 80/5
x = 16
The two legs are 3x = 3*16 = 48 and 4x = 4*16 = 64


area = 0.5*base*height = 0.5*48*64 = <font color=red>1536 square units</font> 
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