Answer
x = √6
Explanation
We will first sketch this triangle.
Let the short leg of the triangle be x
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is θ, the trignometric ratios in short forms are written as
SOH, CAH and TOA
SOH means Sin θ = (Opp/Hyp)
CAH means Cos θ = (Adj/Hyp)
TOA means Tan θ = (Opp/Adj)
So, the one to be used depends on the sides of the triangle that are provided.
For this triangle, using the angle 60° as the non-right-angle angle
Hypotenuse = ?
Opposite = 3√2
Adjacent = x
Angle = 60°
TOA means Tan θ = (Opp/Adj)
Tan 60° = (3√2)/x
Tan 60° = √3
Tan 60° = (3√2)/x
√3 = (3√2)/x
Cross multiply
x = (3√2)/(√3)
x = (√3) (√2)
x = √6
Hope this Helps!!!