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Question 269951: Find the exact value of x (picture included).

Found 2 solutions by Alan3354, dabanfield:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
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x = the altitude, since the right side triangle's upper angle = 45�
x = 34*cos(30) = 17*sqrt(3)

Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
By a theorem the side opposite the 30 degree angle is half the hypotenuse of the right triangle on the left or 34/2 = 17.
The altitude of the triangle on the right is one of the sides of an isosceles triangle with sides equal to x.
By the Pythagorean Theorem we have for the triangle on the left:
34^2 = 17^2 + x^2
x^2 = 34^2 - 17^2
x^2 = 867
x = sqrt(867) = sqrt(289*3) = sqrt(289)*sqrt(3)
x = 17*sqrt(3)