Hello, cedwards08!

Chris, who is 6 feet tall, is walking away from a street light pole 30 feet high

at a rate of 2 ft/sec. .

a. How fast is his shadow increasing in length when Chris is 24 ft from the pole? 30 feet? Code:

*
| *
| *
30 | | *
| 6| *
| | *
*-------*---------------*
: - x - : - - - s - - - :

From the similar right triangles: .

Differentiate with respect to time: .

Therefore: . __always__.

b. How fast is the tip of his shadow moving? Code:

*
| *
| *
30 | | *
| 6| *
| x | y-x *
*-------*---------------*
: - - - - - y - - - - - :

We have: .

Differentiate with respect to time: .

Therefore: . __always__.

c. To follow the tip of his shadow, at what angular rate must Chris

be lifting his eyes when his shadow is 6ft long? Code:

*
| *
| * - - - - -
30 | | * θ
| 6| *
| | θ *
*-------*---------------*
: - x - : - - - s - - - :

We have: .

Differentiate with respect to time: .

. . and we have: . .[1]

We are given: .

From (a), we have: .

When , the right triangle is __isosceles__.

. . Hence: .

Substitute into [1]: .

Therefore, Chris should raise his eyes at the rate of radians/sec.