Question

In triangle abc, we have angle bac = 60 degrees and angle abc = 45 degrees. the bisector of angle a intersects line b at point t, and at = 24. what is the area of triangle abc

Answer 1

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.