Question

HELP ME ANSWER THIS QUESTION!

Boyd (B) is trapped in a soccer training circle. Albert (A) and Carlos (C) kick the ball to Boyd in rotation. Determine how far Boyd needs to kick the ball to Carlos if he is located in the center of his training circle and Carlos is located at the outer rim.

Answer 1

Here we have right-angle triangle. Sides are:
AB = 19+x
BC= x
AC= 30

From the picture we can see that side AB is hypothenuze. We are given number 19 as part of length of that hypothenuze. Other part is equal to distance from center to edge of circle. This length is same as side BC.

We will use Pythagorean theorem to solve this:

`(AB)^(2) = (BC)^(2) + (AC)^(2) \\ (19+x)^(2) = x^(2) + 30^(2) \\ 361+38x+ x^(2) = x^(2) +900 \\ x^(2) - x^(2) +38x=900-361 \\ 38x=539 \\ x=14.2yard`