CPM Homework Help : CALC3RD Problem 7-66

Remember Eric and the $16$ -foot tall lamppost? If Eric (who is $5$ feet tall) walks away from the lamppost at a rate of $4$ ft/sec, at what rate is the tip of his shadow moving away from the lamppost? Draw a diagram before you start this problem.

Diagram:

Right triangle, vertical leg is a lamppost, 2 thirds of the way to vertex opposite vertical leg, is person, standing between horizontal leg & hypotenuse, labeled 5 feet, such that horizontal leg is divided into 2 parts, part between person and right angle labeled, x, other part labeled, s, with title d subscript x divided by d subscript t, = 4.

Step 1:

Use similar triangles to write an equation relating the proportional sides.

Step 2:

Use implicit differentiation to convert the geometric equation into a rate equation.
In other words, find the derivative of everything in terms of time, $t$ .