If Jane walks north for 3 miles, turns 45∘ to the right, and then walks another 4miles, how many miles will Jane be from her starting point? Give your answer as a decimal rounded to the nearest hundredth.

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Answer 1 · 2018-05-23T06:56:37

2.83 miles

The law of cosines says that when finding an unknown side of a non-right triangle, we can use the other two sides such that:

#b^2=a^2+c^2-2(a)(c)(cosB)#

Since we are given the angle corresponding to (or facing) the unknown side measure, we can use our formula such that:

#b^2=3^2+4^2-2(3)(4)(cos45)#
#b^2=9+16-24(cos45)#
#b^2=25-17#
#b^2=8#
#b=sqrt(8)#
#b=2.83" miles"#