I'm having some trouble solving the following problem about heights in a triangle:
- Two of the heights in a triangle do not intersect each other, and the acute angle between their extensions is 45°. Then, which of the following statements is true?
(a) one of the angles of the triangle is 45°;
(b) one of the angles of the triangle is 135°;
(c) it is not possible to determine;
(d) there is no such triangle.
I have attached a diagram of the triangle that I received from someone who tried to help me with the problem. As they explained, if the heights a and c are extended and intersect at a 45-degree angle, the red triangle formed has an angle of 45 degrees (the same applies to heights c and b). However, this does not apply when the heights a and b are extended and intersect at a 45-degree angle. "The answer is therefore C."
Although the explanation was helpful, I still don't understand how to apply it to the problem. Can someone provide a more detailed explanation or guide me on how to solve this problem? Any help would be greatly appreciated.
Thank you in advance!