Question

The hypotenuse of a 30°-60°-90°
triangle has a length of 12 cm.
Which could be the length of a leg
of the triangle?

Answer 1

Answer: Below

Step-by-step explanation:

If you don't know Trigonometry, in a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30° angle and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.  

 

So, since the hypotenuse has length 12 cm,  

 

    side opposite 30° angle (shorter leg) = 6 cm

 

    side opposite 60° angle (longer leg) = 6√3 cm

Answer 2

The possible lengths of the legs are 6 and 6√3

How to determine the length of a leg?

The triangle is given as:

30-60-90 triangle

And we have:

Hypotenuse = 12 cm

A 30-60-90 triangle is a unique triangle with the following parameters

Opposite = Hypotenuse/2

Adjacent = Hypotenuse/2 * √3

So, we have:

Opposite = 12/2

Adjacent = 12/2 * √3

Opposite = 6

Adjacent = 6√3

Hence, the possible lengths of the legs are 6 and 6√3

Read more about right triangles at:

https://brainly.com/question/2437195