Find the length using trigonometry and pythagoras when applicable.

The length of x = 22.69 cm

We can solve this triangle by taking Sin theta because we know that

Sin = Perpendicular / Hypotenuse

We are given with 52 degree and hypotenuse is 23 cm so

Sin 52 = Perpendicular / 23

0.9866 = Perpendicular / 23

0.9866 x 23 = Perpendicular

22. 69 cm

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.