# Thread: Right Triangle Construction

1. ## 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

2. 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.

3. 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 $\frac{\sqrt{3}}{2}\cdot hypotenuse$ , according to Mr. Pythagoras.

Tonio

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# construct a right triangle, having hypotenuse of length 5.4cm and one of the acute angles of measure 30degree.

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