# Right Triangle Construction

• Feb 8th 2010, 05:59 PM
rn5a
Right Triangle Construction
I know how to construct a right triangle when the hypotenuse & one side are given but how do I construct a right triangle whose hypotenuse is 5.4 cm & one of the acute angles is 30 degrees? What are the steps?

Thanks,

Ron
• Feb 8th 2010, 06:05 PM
Quote:

Originally Posted by rn5a
I know how to construct a right triangle when the hypotenuse & one side are given but how do I construct a right triangle whose hypotenuse is 5.4 cm & one of the acute angles is 30 degrees? What are the steps?

Thanks,

Ron

Hi Ron,

If one acute angle is 30 degrees, then the other acute one is (90-30)=60 degrees. You can project these lines away from the hypotenuse until they meet at the right-angled corner.
• Feb 8th 2010, 06:11 PM
tonio
Quote:

Originally Posted by rn5a
I know how to construct a right triangle when the hypotenuse & one side are given but how do I construct a right triangle whose hypotenuse is 5.4 cm & one of the acute angles is 30 degrees? What are the steps?

Thanks,

Ron

Theorem: in a 30-60-90 degree triangle (aka "golden triangle" sometimes), the length of the cathetus in front of the 30 deg. angle is half the hypotenuse's length.
Of course, the other cathetus' length is then $\displaystyle \frac{\sqrt{3}}{2}\cdot hypotenuse$ , according to Mr. Pythagoras.

Tonio