+4 What is the value of x in the diagram?
The diagram:
https://latex.artofproblemsolving.com/2/8/b/28b17b52fcef38528e8b5b98d94cd530c8ee2f7f.png
+128472 The triangle on the left is a 30-60-90 right triangle
Its height = 8 * sqrt (3)/2 = 4sqrt (3) = sqrt (48)
The triangle on the right is a 45-45-90 right triangle.....the altitude and base of this triangle are equal since both are opposite 45° angles
So....by the Pythagorean Theroem
x = sqrt [ (sqrt (48) )^2 + (sqrt (48))^2 ] = sqrt [2 (48)^2 ] = 48sqrt (2)
