Question 1193545
Draw this
There is a right triangle with the hypotenuse the distance to the lighthouse. That angle is 45 degrees east of north.
One of the legs is the distance north to the lighthouse, the other the distance west from the lighthouse. Both of them are the same length in this 45-45-90 triangle, and the distance is 10/sqrt(2)=5 sqrt (2) nm, or about 7.07 nm.