A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point. At a certain moment, the angle between the observer's line of sight and the horizontal is , and it is changing at a rate of 0.5 rad/min. How fast is the balloon rising at this moment? Let y be the height of the balloon (in km), t be time (in minutes), and 0 the angle between the line-of-sight and the horizontal (in radians). (Use decimal notation. Give your answer to two decimal places.)

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.