Now, using the trig ratio for tangent, we see that
........ means the length of the line connecting A and C
So we have
Note thatquestion (b) says: BCi s a quarter circle with centre at (0,0). Line AD has equation y=x.
Also note that the angle the line y = x makes with the x-axis is , or
Using the trig ratio for sine we see that
.........E is the point where a vertical line from D cuts the x-axis, |DE| represents the length of that line
These questions are a bit vague to me. I guess we could do the last one without introducing a new point, if we used the cosine rule or something like that
Given a triangle in plane we can get the and axis anywhere in that plane. So we can get axis passing through and and axis passing through .
Now, if there are two points , then the midpoint of the segment has the coordinates and . Then .
The equation of the line passing through is or
Using one of these equations you can now write the equations of and , then solve the system formed by these equations to find the coordinates of .
Then you can use the distance formula between two points in plane:
to calculate and
It is more clear now?