Sarah and Simone are walking in a walk-a-thon down a straight street that leads to the finish line in the park. At the same time, they both notice a hot-air balloon directly over the finish line. Sarah sees that the angle from the ground to the balloon as 30° and Simone (who is 0.25 km closer to the finish line than Sarah) sees the angle from the ground to the balloon as 45°. a) Draw a diagram to represent this situation.

b) If x represents the distance that Simone is from the finish line, write an expression for the distance from Sarah to the finish line.

c) Write a trigonometric ratio for each girl's position that involves the height of the balloon, h, the distance each girl is away from the finish line, and the angle from the girl to the balloon.