More Triangle Problems, 6

Category: Plane Geometry, Trigonometry

"Published in Newark, California, USA"

Show that, for the two triangles ABC and AXY (see figure),

Photo by Math Principles in Everyday Life

Solution:

Since the altitude of the two triangles are not given, then we can draw the altitudes from points B and X as follows

Photo by Math Principles in Everyday Life

Consider ∆ABC:

but

then the above equation becomes

Consider ∆AXY:

but

then the above equation becomes

Therefore,