In triangle ABC, we have angle BAC = 60 degrees and angle ABC = 45 degrees. The bisector of angle A intersects line BC at point T, and AT = 24. What is the length of side BC?
This is how to solve ABC:
In my estimations you have a triangle with 2 angles and an altitude or height. You have to find the base of the triangle in order to find the area. I set up the triangle and sine the 60 degree angle was bisected I know that the vertex angle is 30 in my right triangle. I used the tangent ratio of 30 to find the base of that triangle and then multiplied it by 2 to get that the whole base measure is 27.71281292. Then I multiplied it by the height I was given of 24 and divided the whole mess in half to get the area. 332.553 units squared.
Somewhere in my explanation I gave a hint to the legnth of BC.