In a 30° -60° -90° triangle, what is the length of the hypotenuse when the shorter leg is 7 in.?

the length of the hypotenuse is 14 in

Step-by-step explanation:

Focus on the 30 degree angle.  Recall that the sine of an angle is defined as

             opposite side        

sin Ф =

                hypotenuse  

and that sin 30° is always 1/2.

                                7 in                               1

Then sin 30° = must equal      

                         hypotenuse                        2

After cross-multiplying this equation, we have 2(7 in) = (1)(hypotenuse),

so that the length of the hypotenuse is 14 in.

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