Question 1185237
the hypotenuse is 2 * sqrt(3).


the angles are 30, 60, and 90.


the  trigonometric functions are:


sin(30) = 1/2


sin(60) = sqrt(2)/3


hypotenuse is equal to sqrt((1/2)^2 + (sqrt(3)/2)^2) = 1


if the hypotenuse is equal to 2*sqrt(3), then all sides need to be multiplied by 2*sqrt(3).


you get:


hypotenuse = 1 * 2 * sqrt(30 = 2 * sqrt(30


side opposite 30 degree angle = 1/2 * 2 * sqrt(30 = sqrt(3)


side opposite 60 degree angle = sqrt(3)/2 * 2 * sqrt)30 = 3


the sum of the sides squared must be equal to the the square of the hypotenuse.


(2 * sqrt(3))^2 = sqrt(3)^2 + 3^2.
simplify to get:
12 = 3 + 9 which becomes:
12 = 12


this confirms the new sizes of the legs are correct when the hypotenuse is equal to 2 * sqrt(3).


the longest leg would be the leg whose length is equal to 3.


here's a reference on 30, 60, 90 degree triangle.


<a href = "https://blog.prepscholar.com/30-60-90-triangle-ratio-formula" target = "_blank">https://blog.prepscholar.com/30-60-90-triangle-ratio-formula</a>


they get the same result a different way.


one of their examples is the  triangle whose hypotenuse is 2 * sqrt(3).


you coculd have gotten the answer either way.