Hello, damselfly!

Consider the shaded region outside the sector of a circle of radius 10 meters

and inside a right triangle. Code:

B *
|:* D
|:::*
h |:* *
|* *
| θ *
C * - - - - - * A
10

a) Write the area of the region as a function of

In right triangle

Area of

Area of sector

Therefore: .

b) What is the domain of the function?

could be any acute angle from 0° to *less than* 90°.

. . .

c) Find: .

Answer: Infinity . . . why?

As increases to , the radius becomes vertical.

Code:

|:::::::::|
|:::::::::|
|:::::::::|
|:::::::* * D
|:::* |
|:* |
|* |
| θ |
C * - - - - * A
10

And the area of the "triangle" becomes infinite.