1) A circle has a diameter of \(36\). Two radii are drawn such that they form a \(30^{\circ}\) central angle. Find the area of the triangle that is formed by connecting the two endpoints of the two radii.
3) Find the area of a segment of a circle with radius \(15\) and a central angle of \(42^{\circ}\).
5) Tracy has a \(9\) meter by \(12\) meter lawn that she wants to water. She has two sprinklers, each of which can water grass within an \(8.4\) meter radius. Tracy wants to set up the two sprinklers so that they are on corners of the lawn. She would like for the sprinklers to water as much of the lawn as possible. Tracy has been given two different options for placing the sprinklers. One option is to put the sprinklers at opposite ends of a \(12\) meter side of the lawn. The other is to put the sprinklers at opposite corners of the lawn. (See the figures below.) Which strategy appears to be best? Justify your answer.