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Given:
with altitude h shown in the diagram. The altitude is perpendicular to
.
Prove: Area of
A diagram of the triangle ABC. A perpendicular line is drawn from the top vertex A to the base BC. The length of AC is b, AB is c, BC is a, and the length of the perpendicular line is h.
By the definition of the
, the area of
is
. Then,
by the definition of the sine ratio. Using the
division property of equality
,
. Lastly
by the
.
