In a right triangle OAB, OA and AB are the legs, OB is the hypotenuse.
The area of a right triangle is equal to half of the multiplication of the lengths legs:
`S▲=1/2*AB*OA`
For example, if the opposite side is 2 and the adjacent side is 4, then the area will be 0.5*2*4=4
As you can see, if the angle tends to 0, then the opposite side will tend to 0 and the area of the triangle will tend to 0
And in the same way, if the angle tends to 90 degrees, then the length of the adjacent leg will tend to 0 and the area of the triangle will also tend to 0
The maximum area of a right triangle with a fixed hypotenuse is formed for an angle of 45°
Area of a triangle in a unit circle
What is the relationship between the area of a triangle on the unit circle and the area in a right triangle? The radius OB, its projection OA on the x-axis and the segment AB connecting the radius and the projection form such a right triangle. The radius is the hypotenuse, its projection OB is the adjacent side, segment AB is the opposite side. The segment AB is equal to the projection of the radius onto the y-axis. Segment OA is the projection of the radius onto the x axis. If we consider a circle with radius 1, then the hypotenuse is equal to 1, AB is equal to the sine of the angle, and OA is equal to the cosine of the angle. And the area of a triangle is equal to half the product of the sine of the angle and the cosine of the angle.