Alan drove 260 miles using 12 gallons of gas. at this rate, how many gallons of gas would he need to drive 286 miles?

Alan would need 13.2 gallons of gas to drive 286 miles.  

Step-by-step explanation:

This question can be solved in a number of ways.  First, you can find the unit rate, or the approximate amount of miles that Alan can drive per gallon of gas.  Since we know that Alan drove 260 miles using 12 gallons of gas, we can divide the number of miles by the number of gallons to get the amount of miles per gallon:  260 ÷12 = 21.67miles per gallon.  In order to find the amount of gas needed to drive 286, we take the total mileage divided by the unit rate:  286 ÷ 21.67 = 13.2 gallons.  The other way to solve is using a proportion with a variable, for example:  260/12 = 286/x.  Using cross-multiplication and divide, we get 260x = 3432, divide both sides of our equation by 260 to isolate the variable and solve for x = 13.2  Either method will result in the same answer.  

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)