[color=#000000]Interact with the applet below for a few minutes.  Be sure to move the [b]LARGE BLACK VERTICES[/b] around before each time you re-slide the slider. [/color][br][br][color=#000000]After interacting with this applet, please answer the questions that follow.  [/color]

[color=#000000][b]Questions:[/b][br][br]1) Suppose the shorter leg of a 30-60-90 triangle is 2 inches long. [br]    Find the length of its longer leg.  Write this length in simple radical form. [br][br]2) Suppose the shorter leg of a 30-60-90 triangle is 3 inches long. [br]    Find the length of its longer leg.  Write this length in simple radical form. [br][br]3) Suppose the shorter leg of a 30-60-90 triangle is 4 inches long. [br]    Find the length of its longer leg.  Write this length in simple radical form. [br][br]4) Suppose the shorter leg of a 30-60-90 triangle is 5 inches long. [br]    Find the length of its longer leg.  Write this length in simple radical form. [br][br]5) Suppose the shorter leg of a 30-60-90 triangle is 6 inches long. [br]    Find the length of its longer leg.  Write this length in simple radical form. [br][br][i]Notice any patterns?  If so, describe.  [br][br][/i]6) Suppose the shorter leg of a 30-60-90 triangle is [i][b]a[/b][/i] units long. [br]    What would the length of its hypotenuse be (in terms of [i][b]a[/b][/i]) ?  [br]    What would the length of its longer leg be (in terms of [i][b]a[/b][/i])?  [br][/color]