Quandaries and Queries
 

 

How do you find the length of the hypotenuse of a 30-60-90 triangle when the side opposite the 60 degree angle is 6 inches?
 
Amy
Student
Secondary
 

 

Hi Amy,

What I remember is that for a 30-60-90 triangle the sides are in the ratio of

1:2:sqrt(3)

2 is the largest of the three numbers so it is the length of the hypotenuse, and 1 is the smallest of the three numbers so it is the length of the side opposite the 30o angle.

In your triangle the length of the side opposite the 60o angle is 6 inches. In my triangle the length of that side is sqrt(3) inches. Thus the sides in your triangle are 6/sqrt(3) times as large as the sides in my triangle. Hence your triangle has side lengths

1  6/sqrt(3) =  6/sqrt(3)

2  6/sqrt(3)12/sqrt(3) and

sqrt(3)  6/sqrt(3) = 6

Penny

 
 

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