The hypotenuse of a 30 -60 -90 triangle is 13cm. What is the length of the shorter leg?

(13/2) cm

Step-by-step explanation:

The hypotenuse here is of length 13 cm.  The shorter leg lies opposite to the 30° angle.  Recall that the sine function is defined as

              opposite side

sin Ф =

                 hypotenuse

which, in this case, works out to:

                opposite side

sin 30° =

                       13 cm

and so the length of the opposite side (which is also the "shorter leg") is

shorter leg length = (13 cm)(sin 30°) = (13 cm)(1/2) = (13/2) cm

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