Answer:
x= ~8.69
solve with law of sine:
law of sine essentially states that
(side length)/(sine of opposite angle) are in the same ratio as another (side length)/ (sine of its opposite angle)
right angles =90 degrees
line QS is opposite to angle R
so
QS/ (sin 90)
9/ (sin 90)
line RS is opposite to angle Q
measure of angle Q= 75 degrees
RS/ (sin 75)
x/ sin (75) RS is x
and these ratios are equal according to law of sine
9/ (sin 90)= x/ sin (75)
sin 90=1
sin 75 = approx ~0.9659
4th decimal place for accuracy, will round more later
9/ (sin 90)= x/ sin (75)
9/ 1= x/ 0.9659
9= x/ 0.9659
x=8.6931
round to nearest tenth
8.6931
~8.69
hope this helps !!