How much string is out if a kite is 100 feet above the ground and the string makes an angle of 65° with the ground?

You have a right triangle situation here, and what you are looking for is the length of the hypotenuse. The leg perpendicular to the ground is 100, and the base angle that is NOT the right angle, is 65. So your equation is set up like this: sin 65 = 100/x. Rearrange that a bit to get x alone: x = 100 / sin 65. Make sure your calculator is in degree mode and solve for x. x = 110.34 feet of string.