Question 813263
It might help if you draw a diagram:<ol><li>Draw a triangle and label the vertices A, B and C.</li><li>Label side AC as 43 feet.</li><li>Label angle BAC as 105 degrees.</li><li>Label angle BCA as 42 degrees.</li><li>Label side BC as x (since that is what we are looking to find).</li></ol>Probably the easiet way to find x is to use the Law of Sines. This will require that we know what the angle opposite side AC is. Using the fact that the three angles add up to 180 we should be able to use the other two angles to find the third one. The third angle, ABC, is 33 degrees.<br>
Now we are ready to use the Law of Sines:
{{{sin(33)/43 = sin(42)/x}}}
Cross-multiplying we get:
{{{x*sin(33) = 43*sin(42)}}}
Divide by sin(33):
{{{x = (43*sin(42))/sin(33)}}}
I'll leave it up to you and your calculator to simplify the right side.