Let A = (0,3) and B = (4,0) and AB = 5 = c
Let D be the altitude to the hypotenuse.
a) Find the coordinates of D
b) Find the lengths of AD, BD, and CD
ABC is a 3-4-5 triangle, so angle A = 53.1 degrees, angle B = 36.9 degrees.
Since CD is the altitude, we know that it is perpendicular to AB, so angle CDB is 90 degrees.
Therefore, angle DCB is 180 - 90 - 36.9 = 53.1, then angle ACD must be 36.9 degrees.
Now, you can see that ...
The expert finds the coordinates and length of different lengths with a hypotenuse.