Problem:
How many triangles have area and vertices at , and for some angle
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The area of the triangle is (base)(height) . There are four values of between and for which , and each value corresponds to a distinct triangle with area .
The vertex lies on a circle of diameter centered at the origin. In order that the triangle have area , the altitude from that vertex must be . There are four points on the circle that are units from the -axis.