a problem of trigonometry

Question

θ is an acute angle in a right triangle. If θ =45º and the hypotenuse has length 5299, how long is the side adjacent to θ? Give answer in exact form.

Answer 1

5299= (sqr2)(a)

a = 5299/sqr2 in exact form

= about 3746.9588

although the question is slightly ambiguous, as the side adjacent to 45 degrees could be either the hypotenuse or the other side. so if it's the hypotenuse, then that side adjacent to theta=45 is 5299, exactly

but it's an isoscelese right triangle with 2 smaller equal sides, each equal to hypotenuse over square root of 2

h^2 = a^2 +b^2

5299^2 = a^2 +a^2

5299^2 = 2a^2

a^2 = 5299^2/2

a = 5299/sqr2