A man 7

A man wandering in the desert walks 3.8 miles in the direction S 44° W. He then turns and walks 2.2 miles in the direction N 55° W. At that time, how far is he from his starting point? (Round your answer to two decimal places.)

Correct answer:

d =  4.68 mi

Step-by-step explanation:

α=180+44=224  a=3.8 mi β=36055=305  b=2.2 mi  x1=a sinα=a sin224° =3.8 sin224° =3.8 (0.694658)=2.6397 mi y1=a cosα=a cos224° =3.8 cos224° =3.8 (0.71934)=2.73349 mi  x2=b sinβ=b sin305° =2.2 sin305° =2.2 (0.819152)=1.80213 mi y2=b cosβ=b cos305° =2.2 cos305° =2.2 0.573576=1.26187 mi  x=x1+x2=(2.6397)+(1.8021)4.4418 mi y=y1+y2=(2.7335)+1.26191.4716 mi  d=x2+y2=(4.4418)2+(1.4716)2=4.68 mi

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