tanX is 12/5.
Given:
In a right triangle,
The length of the side <em>XY</em> = 13.
The length of the side <em>YZ</em> = 12.
The length of the side <em>XZ</em>= 5.
The objective is to find tan <em>X</em>.
In a right angled triangle the largest side is always hypotenuse.
Sinec tan <em>X</em> is required to solve, then, the side <em>YZ </em>is opposite side and the side <em>XZ</em> is adjacent side.
By the trigonometric ratios, the value of tan <em>X</em> can be calculated as,

Hence, the value of tanX is 12/5.
Let Sydney's age be x
Christine's age is 2x
Sum of their age is 54
x + 2x = 54
3x = 54
x = 18
Sydney is 18 years old.
10 glasses can be filled to the top
and 11 glasses if you want to now how i got it divide by 12.
Answer:
Use a compass to measure the length of AB.
Draw an arc from point B (or point A) with that distance.
Extend line AB through that arc and label the intersection as point C.
AC is twice the length of AB.
She has to add 2 more quarters for 108 more days.