When there is moisture on the ground, microorganisms inhabit the thin layer of water on leaves. ${ }^4$ A monolayer containing these organisms is formed on the top, and (because of the spreading pressure of this monolayer) the floating organisms spread upward when the surface is tilted. This is a dispersal method onto newly fallen leaves, for example. In the accompanying diagram, the horizontal segment represents the ground, and the angle $\theta$ measures the amount by which the surface is tilted. (We assume that $\theta$ is less than $90^{\circ}$.) The length $d$ is the distance the organisms move, and the length $v$ is the change in the elevation.
GRAPH CAN'T COPY.
a. Find a formula giving $v$ in terms of $d$ and $\theta$.
b. Assume that the distance the organisms move is 30 centimeters. Find the change in elevation if the angle $\theta$ is $15^{\circ}$ and if the angle $\theta$ is $30^{\circ}$.
c. Find the angle $\theta$ if the distance the organisms move is 30 centimeters and the change in elevation is 20 centimeters.