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The altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

 Nov 13, 2018
 #1
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Using the "Law of Sines" we have:

The hypotenuse of the large triangle =4sqrt(3)

The shorter side to the right =2sqrt(3)

The Base to the left =6

Area of the large triangle =1/2 x 6 x 2sqrt(3) =6sqrt(3) units^2.

 Nov 13, 2018
 #2
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+1

The triangle on the "left"  has a base  =   3sqrt (3)

The triangle on the "right" has a base = 3 / sqrt (3)  =  3sqrt (3) / 3   =  sqrt (3)

 

So.....the area  =

 

(3) [ 3 sqrt (3)  + sqrt (3) ]   / 2   =

 

3 [ 4sqrt (3) ]  / 2   =

 

3 [ 2 sqrt (3) ]  =

 

6sqrt (3)  units^2

 

 

cool cool cool

 Nov 14, 2018

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