Question

Find the exact values of x and y.

Answer 1

The hypoteneuse is the angle opposite the right angle so from right triangle trigonometry we have \[x=rcos( \theta)\] and \[y = rsin( \theta)\]

Answer 2

alternative :

the proportion the length of sides a 45-45-90 triangle is 1:1:sqrt(2)
so, x=y
and to get x or y, use
x sqrt(2) = sqrt(21)
x = sqrt(21)/sqrt(2)
then u need rationalize that fraction : (multiply by sqrt(2)/sqrt(2))
x = sqrt(21)/sqrt(2) * sqrt(2)/sqrt(2)
x = sqrt(21*2)/2 = sqrt(42)/ 2