The hypotenuse of a right-angled triange has the length of 10cm.
Find an expression for the area of the triangle in terms of
For what value of is the area a maximum and what is this maximum area?
A right triangle can be inscribed in a semicircle.
* * * C
* * :**
* * h: **
* θ : *
A * - - - - - - - + - * B
The base of the triangle is 10.
Hence, the area is: .
The area is a maximum when is a maximum.
. . This occurs when (radius) . . .
Therefore, the maximum area is: .