A SHIP TRAVELS 60 MILES DUE EAST THEN ADJUST ITS COURSE 15 DEG. NORTHWARD AFTER TRAVELING 80 MILES IN THAT DIRECTION, HOW FAR IS THE SHIP FR

We could also use the Law of Cosines to find this. Note that the supplementary angle to "15° northward" is 165°

So we have

√[80² + 60² - 2(80)(60)cos(165°)] = 138.83 miles

Total eastward distance E = 60 + 80*cos(15°)

Total northward distance N = 80*sin(15°)

Total distance from origin D = √(E² + N²)

$${\mathtt{D}} = {\sqrt{{\left({\mathtt{60}}{\mathtt{\,\small\textbf+\,}}{\mathtt{80}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{15}}^\circ\right)}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\left({\mathtt{80}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{15}}^\circ\right)}\right)}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{D}} = {\mathtt{138.826\: \!827\: \!135\: \!014\: \!3}}$$

D ≈ 138.8 miles

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