Question

The shorter leg of a 30°-60°-90° triangle is 6. What is the length of the other leg?

Answer 1

The length of the other leg is 12, I think, but I'm not sure. Sorry if it's wrong.

Answer 2

`x=6√(3)` units.

Explanation:

It is given that shorter leg of a 30°-60°-90° triangle is 6.

In a triangle larger interior angle has larger opposite side and vice versa.

The length of shortest leg is 6 units it means it is opposite to the angle 30°.

Let the length of second leg be x.

In a right angle triangle,

`\tan \theta =\frac{\text{Opposite}}{\text{Adjacent}}`

`\tan (30^\circ) =(6)/(x)}`

`(1)/(√(3))=(6)/(x)}`

On cross multiplication, we get

`x=6√(3)`

Hence, the length of the other leg is
`x=6√(3)` units.