Question

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

Answer 1

The equation which can be used to determine the minimum and maximum optimal angles of launch is:

|x – 45| = 3

and the minimum angle that is still optimal is:

42 degrees.

Explanation:

Let x be the optimal angle by which the balloon is launched.

Also, it is given that the they launch the balloon at an angle within 3 degrees of 45 degrees.

i.e. the range at which the angle is launched lie between 3 degree less than 45 degree and 3 degree more than 45 degree.

Hence, the equation that will represent this relationship is:

|x-45|=3

Hence, on solving for the maximum value we have:

`x-3=45\\\\i.e.\\\\x=45+3\\\\i.e.\\\\x=48\ degree`

and the smallest optimal angle is given by:

`x-45=-3\\\\i.e.\\\\x=45-3\\\\i.e.\\\\x=42\ degree`

Answer 2

|x - 45| = 3; minimum angle: 42 degrees