Jo drops a marble from her apartment window, 20 meters above the ground. At the s ame height bu' 12 meters away, Doe watches the marble fall. When the height of the marble above the ground is h let 0 be the angle between L and M, where L is the horizontal line joining Jo and Doe, and where M represents Doe's line of sight to the marble. (a) Draw a picture of the scene, including L, M, and 0. Put the horizontal axis at ground level and indicate the position of the marble h(t) meters above ground level at time t. (b) Find 0 in terms of h, and then calculate de/dh. (c) Assume that h(t) = 20– 4.9t² until the marble hits the ground. Find d0/dt. Show geometrically why de /dt > 0, and then tell why the formula for de/dt tells us that in fact de/dt > 0. Note: It turns out that there is a value to for which de/dt has a maximum value. For 0(to) the marble appears to be falling the fastest. Can you find the value of to?

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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.