Question

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

Answer 1

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.