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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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

Explanation:

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:

$b^{2} = a^{2} + c^{2} - 2 (a) (c) (cos B)$ $b^2=a^2+c^2-2(a)(c)(cosB)$

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

$b^{2} = 3^{2} + 4^{2} - 2 (3) (4) (cos 45)$ $b^2=3^2+4^2-2(3)(4)(cos45)$
$b^{2} = 9 + 16 - 24 (cos 45)$ $b^2=9+16-24(cos45)$
$b^{2} = 25 - 17$ $b^2=25-17$
$b^{2} = 8$ $b^2=8$
$b = \sqrt{8}$ $b=sqrt(8)$
$b = 2.83 miles$ $b=2.83" miles"$

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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.

1 Answer

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