What do you want to find out, for drawing a triangle we need to know three elements?
I have a triangle with two vertices known (1,3) and (-4,1).
I know a formula relating the acute angle formed by two lines and their slopes. It is
I used this formula for the hypotenuse and one of the sides(m1) and then again used this formula for the hypotenuse and the other side(m2). I used the result m1m2=-1 in the second result and got two values of m1. But when I equate those values I get tanA=0.
What is wrong?
Please show your work that will make this clear. In fact where are the slopes of tow other sides of the triangle? I Sri think some information is missing. With only this much information we gat infinitely many triangles and hence the problem?
there is no other information. I don't know what I am doing wrong with the information that is provided.
slope of hypotenuse=2/5
putting this in the formula for tan A.We get
Similarly, I found m2 in terms of tan A and replaced m2 with -1/m1 to get
On equating these two values of tanA I get tanA=0.
appears to be the slope of a vertical line. But, if it is not, then you can calculate it using . (note: this slope is not defined if ).
Then appears to be the slope of a horizontal line. Still, we can calculate it: (note: this slope is not defined if ).
Then, you would have
Simplifying, you get
Is that what you were looking for?
Oh, I misread the problem. This may not be the solution. The calculation I gave was for the angle between the lines with slopes , not angle . Also, if you are suggesting that the two lines are perpendicular, then
So, possibly this would be helpful The second equation just came from finding the length of each segment.
Then, simplifying the LHS and squaring both sides, you have:
Apparently, this has solutions at over the integers, and over the reals, it has solutions or and .