Question

let S be a square, let M and N be the midpoints of two adjacent sides, and let V be the corner of the square that is opposite both M and N. Let θ be the measure of the angle between the two lines connecting M and N with V. Compute sin(θ).

Answer 1

If we have a basis of 2 units for the length of the side of the square,
then MV = NV = 1

Using pythagoeran theorem
MN = sqrt (MV^2 + NV^2)
MN = sqrt(2)

Therefore,
sin θ = 1 /√2
or
sin θ = √2 / 2