The shorter leg of a 30°-60°-90° triangle is 6. What is the length of the hypotenuse?

1 Answer
Shwetank Mauria
Nov 22, 2016

Length of hypotenuse is #12#

Explanation:

The leg of a 30°-60°-90° triangle are in the ratio of #1/2:sqrt3/2:1#. Here if the hypotenuse being largest is opposite #/_90°# is #x# and is double the smallest side opposite #/_30°#, which is #x/2# and third side opposite #/_60°# is #sqrt3/2x#.

This is as such a triangle if doubled as shown below becomes equilateral triangle.
enter image source here

As smallest side, opposite #/_30°#, is #6#

length of hypotenuse is #6xx2=12#

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