The diagram shows part of a glass structure. PQRS is a horizontal square with sides of 1 metre, and point X is 4 metres vertically above P. What is the cosine of the angle that XR makes with the horizontal?

Answer:

The angle required is XRP
Using Pythagoras theorem PR = √2, since PR
is a diagonal of square PQRS.
Then triangle XPR is a right angled triangle as X is
vertically above P, and by Pythagoras XR = √18 = 3√2
then cos(𝑋𝑅𝑃) = 𝑃𝑅/𝑋𝑅 = √2/3√2 = 1/3
The answer is A