Step-by-step explanation:
imagine an inner right-angled triangle.
QW is the Hypotenuse (the side opposite of the 90° angle).
QP is one leg. = 9 cm.
PW is the second leg (and the diagonal of the base rectangle).
the angle of QW to PTWS is the angle W in this triangle.
we get PW by Pythagoras
PW² = 5² + 7² = 25 + 49 = 74
PW = sqrt(74)
QW we get now also via Pythagoras :
QW² = 9² + (sqrt(74))² = 81 + 74 = 155
QW = sqrt(155)
since we have a right-angled triangle, we know that the legs are sine and cosine of W (multiplied by QW).
so,
9 = sin(W)×sqrt(155)
sin(W) = 9/sqrt(155) = 0.722897396...
W = 46.29421586...° ≈ 46.3°
the angle of QW with PTWS is 46.3°.
