The longer leg of a 30°-60°-90° triangle measures [tex]9\sqrt{3}[/tex] inches. What is the length of the shorter leg? A. 18 inches B. [tex]18\sqrt{3}[/tex] inches C. [tex]9\sqrt{3}[/tex] inches D. 9 inches

Answer:D. 9Step-by-step explanation:The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x).  The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse).  If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:9√3 = x√3 and solve for x.  Divide both sides by the √3 to get that x = 9