Whats the relationship between an angle and and the ratio of sides in a right triangle?

Question

geometry_hater · Answer

its for an activity here http://hotmath.com/util/hm_flash_movie.html?movie=/learning_activities/interactivities/triangleSlopeRatio.swf&return_to=Geometry%20Activities&title=Slope%20Triangles

asnaseer · Answer

in the right-angled triangle shown there, the relationship between the angle in red (lets call it theta) and the ratio of the sides dy and dx is:$$\tan(\theta)=dy/dx$$
the equation of a straight line can be written as:$$y=mx+c$$where m represents the slope of the line. if you know the angle of the slope, then this can also be written as:$$y=x\tan(\theta)+c$$where theta is the angle the line makes with the horizontal.
I hope this helps you understand the activity.