The shorter leg of a 30°−60°−90° triangle is 4 in. Find the hypotenuse and the other leg. The length of the hypotenuse is in. The length of the other leg is in.

The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.

Step-by-step explanation:

Note that tan 60 degrees = (length of longer leg) / (length of shorter leg), or

                tan 60 degrees = (length of longer leg) / 4 in.

Thus, (length of longer leg) = (4 in)(tan 60 degrees)

                                              = (4 in) [√3/1] = 4√3 in

Also, cos 60 degrees = (adjacent side) / (hypotenuse.  We want to find the hypotenuse and thus solve this equation for it:

(hypotenuse) = (adjacent side) / (cos 60) = (4 in)( 2/1 ) = 8 in

The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.

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