Question

Question #bc494

Answer 1

The relationship between variables gives you the relationship between the rates.

Explanation:

The ladder (hypotenuse) is 14' long.
Let the vertical side of the triangle be x (so that `dx/dt = -2`).
Let `theta` be the angle between the top and the house.

Then there is a relationship between x and `theta` given by the triangle. In the triangle, x is adjacent to `theta`, and 14 is the hypotenuse.
Therefore `cos(theta) = x/14`, or
`x = 14cos(theta)`.
Differentiate both sides with respect to t.
`dx/dt = -14sin(theta)(d(theta)/dt)`
Substitute -2 for the left side.
NOW use the fact that x = 12 at the moment.
Use trig identities to find the value of `sin(theta)` when x = 12.
The equation above will now have only one unknown. Solve for it.