SOLUTION: Find the value of y. A 30, 60, 90 degree right triangle is drawn. The 60 degree angle is labeled. The shortest leg adjacent to the 60 degree angle is labeled x. The longest leg op

Algebra ->  Triangles -> SOLUTION: Find the value of y. A 30, 60, 90 degree right triangle is drawn. The 60 degree angle is labeled. The shortest leg adjacent to the 60 degree angle is labeled x. The longest leg op      Log On


   

Question 469408: Find the value of y.
A 30, 60, 90 degree right triangle is drawn. The 60 degree angle is labeled. The shortest leg adjacent to the 60 degree angle is labeled x. The longest leg opposite the 60 degree angle is labeled 5 times the square root of 3. The hypotenuse is labeled y.
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
For the special 30-60-90 right triangle, the corresponding sides are:
a, sqrt%283%29a, 2a
So the hypotenuse is always twice the length of the short leg, and the long leg is sqrt%283%29 times the short leg.
For this problem the short leg is x.
Therefore hypotenuse y is 2x, y = 2x
Therefore long leg is sqrt%283%29x
5sqrt%283%29+=+sqrt%283%29x
Divide by sqrt%283%29 on both sides
5+=+x
Therefore, y = 2*5 = 10