I am to find "d" (the hypotenuse)in the simplest radical form of a right triangle. The two angles are 30 degrees on top and the on the bottom is 60 degrees. Of course the opposite side to the left of 60 is 90 degrees. My options are:

Question

A) 8sqrt3
B) 4
C) 8sqrt2
D) 16

I do not know how to figure this out

Answer 1

Since they did not give the length of
either side of the triangle, you'll
have to create a unit(1)triangle and
select d based on the INFO given.
let d=1, Y=1Sin60=0.8660=(sqrt3)/2=
side opp. 60 deg.angle, X=1Cos60=1/2=
side adj. to 60 deg. angle.The triangle is to be in simplest radical form. However, all sides must be multiplied by 4: d=4(1)=4, Y=4(sqrt3)/2
=2(sqrt3). So d=4 the smallest choice.

Answer 2

find ab in simplest form if A(0,3) and B(2,7)