Question

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

Answer 1

the length of the hypotenuse is 14 in

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.