Expert: Sherry Wallin - 7/22/2011

Question
QUESTION: If you have a right triangle as shown in the graph below,

I guess it is possible to calculate the slope from the intersection points of the line but is it possible to calculate the other angles then?

x1,x2,y1,y2 are all known but angles A,and B are not.

Thank you

ANSWER: Nelaw~
You can find the distance between two points and that will give you the length of the hypotenuse, call it x,  then angle sin A is opp/x and angle sin B = opp/x. Now in the first A = arcsin(opp/x) and in the second B = arcsin(opp/x)

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Thank you for your response

But in my case the length of opp is not known nor the other side . Actually the only known things in the triangle is x1,x2,y1,y2

Thanks again

Answer
Nelaw~

If you know x1,x2,y1,y2 you can find the distance between the two ordered pairs (x1,y1) and (x2,y2) which will be the length of the hypotenuse (distance) between both points.

Hypothetically, say I know the points (2,3) and (3,6) then the hypotenuse or the distance between the two points is
sqrt[(x2-x1)^2 + (y2-y1)^2] => sqrt[(3-2)^2 + (6-3)^2] => sqrt[1+9) => sqrt(10) which is the length of the hypotenuse as well as the distance between (x1,y1) and (x2,y2)

Now you have enough information to find the measure of angle A and angle B in the following way:
in this particular case where I chose the points (you say you know them already but have not given them to me) then your x coordinate changes by 1 so one leg of the right triangle is 1 and the y coordinate changes by 3 so the other leg is 3. You now have a right triangle with known values of the legs 1,3 and hypotenuse sqrt(10). So the sin A = 1/sqrt(10) =. A = arcsin(1/sqrt(10))  about 18.43 degrees and sin B = 3/sqrt(10) =>
B = arcsin(1/sqrt(10)) about 71.57 degrees. Of course once you knew the measure of angle A all you really have to do is 90- m<A = m<B
I took the inverse of the sine function on both sides of the equation to get the angle by itself.

Math Prof

Or the length of one of the legs is x2-x1 and the length of the other leg is y2-y1 and the distance or length of the hypotenuse is
sqrt[(x2-x1)^2 + (y2-y1)^2]