Marion is using a computer-aided drafting program to produce a drawing for a client. she begins a triangle by drawing a segment 4.2 inches long from point A to point B. from B, she moves 42 degrees counterclockwise from the segment connecting A and B and draws a second segment that is 6.4 inches long, ending at point C. to the nearest tenth, how long is the segment from C to A?
+130511 So we have something like this :
Let's use the Law of Cosines to confirm that the length of AC is correct. So we have:
$${\left({{\mathtt{6.4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{4.2}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{6.4}}{\mathtt{\,\times\,}}{\mathtt{4.2}}\right){\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{138}}^\circ\right)}\right)}^{{\mathtt{0.5}}} = {\mathtt{9.927\: \!309\: \!092\: \!480\: \!374\: \!7}}$$
And to the nearest tenth, we have 9.9 inches
+130511 So we have something like this :
Let's use the Law of Cosines to confirm that the length of AC is correct. So we have:
$${\left({{\mathtt{6.4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{4.2}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{6.4}}{\mathtt{\,\times\,}}{\mathtt{4.2}}\right){\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{138}}^\circ\right)}\right)}^{{\mathtt{0.5}}} = {\mathtt{9.927\: \!309\: \!092\: \!480\: \!374\: \!7}}$$
And to the nearest tenth, we have 9.9 inches
