what is the length of the hypotenuse of a 30-60-90 triangle if the side oppostie the 60-degree angle is 6sqrt3?
In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half of the length of the hypotenuse, and the length of the side opposite the 60-degree angle is (sqrt(3)/2) times the length of the hypotenuse.
Let x be the length of the hypotenuse.
The length of the side opposite the 60-degree angle is (sqrt(3)/2) * x, and in this case, it is given as 6sqrt3.
Therefore, (sqrt(3)/2) * x = 6sqrt3
Simplifying the equation, we have:
sqrt(3) * x = 12sqrt3
x = 12
The length of the hypotenuse of the 30-60-90 triangle is 12.