The shorter leg of a 30°- 60°- 90° right triangle is 7.5 inches. How long is the longer leg and the hypotenuse?

1 Answer
Alan P. · Meave60
Jun 8, 2015

The longer leg is #7.5 sqrt(3)# inches.
The hypotenuse is #15.0# inches.

Explanation:

A right triangle with angles #30^@-60^@-90^@# is one of the standard trigonometric triangles with sides in the ratio:
#color(white)("XXXX")##1:sqrt(3):2#

If the shortest side is 7.5 inches,
the other two sides are
#color(white)("XXXX")##7.5sqrt(3) and 15.0# inches.

![http://commons.m.wikimedia.org/wiki/File:30-60-90_triangle.svg](useruploads.socratic.org)

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