Question

Twenty minutes after being launched, a hot-air balloon has risen to an altitude of 300 m. The pilot can still see the starting point on the ground at a 25° angle of depression. How many meters is the balloon from the starting point?

Answer 1

Angle of depression is the angle below the horizontal that an observer must look in order to see an object below him. If you draw the figure, you can actually see that the hot-air balloon is located 25° above the horizontal.
We actually formed a triangle here, with height equal to 300, unknown base and 25° angle between the hypotenuse and base. What we need to find here is the length of hypotenuse (which is also the distance from the starting point to the balloon). Let x = hypotenuse. We shall use sine:
sin (angle) = opposite/hypotenuse
sin 25° = 300 / x
x = 300 / sin 25°
x = 709.9 m

Hope this helps~ :3