The hypotenuse of a 30°-60°-90° triangle measures 6/3 inches . What is the length of the longer leg?

1 Answer
Hriman · Emily
Apr 20, 2018

#sqrt3" in"#

Explanation:

In a #30-60-90# special right triangle:

Side opposite to #30# degrees: #x#
Side opposite to #60# degrees: #xsqrt3#
Side opposite to #90# degrees: #2x#

So, in this case, we must find the side opposite to the #60# degrees, because the hypotenuse (given in the question) is always the opposite side of #90# degrees, and the shortest side is always opposite to the shortest angle (in this case, #30# degrees).

First, we can use the given hypotenuse value and the expressions above to solve for #x#, the shortest leg length.

#2x= 2 " in"#

#x= 1 " in"#

Therefore, the longer leg:

#xsqrt3= sqrt3 " in"#

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