Side Lengths of the Unit Triangles

Since the Unit Circle has radius=1 unit, the special right triangles that exist in the Unit Circle all have a hypotenuse=1 unit.

We can determine the [b]side[/b] [b]lengths of each unit triangle[/b].[br][br]Each square root expression has been converted to decimal form for your reference.[br]Notice the labeled side lengths on each triangle.[br]The applet also shows calculated side length ratios within each triangle.[br][br]Click "Unitize" to make the hypotenuse equal to 1 (as it would be in the Unit Circle)[br][color=#c51414][b]Unitize each of the triangles to determine the side length values used in the Unit Circle.[/b][/color]

Which of the following side lengths exist within the "unitized" version of the 45-45-90 triangle?

[math]\frac{\sqrt{2}}{2}[/math] (approximately 0.707 as a decimal) [math]\frac{\sqrt{3}}{2}[/math] (approximately 0.866 as a decimal) 1 [math]\frac{1}{2}[/math]

Which of the following side lengths exist within the "unitized" version of the 30-60-90 triangle?

[math]\frac{\sqrt{3}}{2}[/math] (approximately 0.866 as a decimal) [math]\frac{\sqrt{2}}{2}[/math] (approximately 0.707 as a decimal) 1 [math]\frac{1}{2}[/math]

In the 45-45-90 triangle, both LEGS are equal to ________________.

1 [math]\frac{\sqrt{3}}{2}[/math] (approximately 0.866 as a decimal) [math]\frac{1}{2}[/math] [math]\frac{\sqrt{2}}{2}[/math] (approximately 0.707 as a decimal)

In the 30-60-90 triangle, the SHORT LEG is equal to ________________.

[math]\frac{1}{2}[/math] [math]\frac{\sqrt{2}}{2}[/math] (approximately 0.707 as a decimal) 1 [math]\frac{\sqrt{3}}{2}[/math] (approximately 0.866 as a decimal)

In the 30-60-90 triangle, the LONG LEG is equal to ________________.

[math]\frac{1}{2}[/math] [math]\frac{\sqrt{3}}{2}[/math] (approximately 0.866 as a decimal) [math]\frac{\sqrt{2}}{2}[/math] (approximately 0.707 as a decimal) 1