To get to her friend's house, Sandra walked along the sidewalk in her neighborhood. If she walked 100 yards at a direction of 45 degrees northeast and then turned to walk 400 yards straight east, how many yards and in what direction would she need to walk if she walk if she wanted to walk straight home without having to make any turns? Round any irrational answers to one decimal place.

Question

anonymous · Answer

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directrix · Answer

Do you think that the angle at the apex of the triangle is (90 + 45) = 135 degrees? I'm just wondering.

anonymous · Answer

I just realized that, I didn't put any angles in...I was staring at it thinking "I need more information..." And I have it...i'm sorry I'm moronic.

anonymous · Answer

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directrix · Answer

I am moronic, too. 135 + 45 would leave no degrees for the third angle.

anonymous · Answer

:) Well I'm glad I'm not the only one making stupid mistakes.

directrix · Answer

Have you studied the Law of Sines or the Law of Cosines?

anonymous · Answer

working on that now... $$c ^{2}=a ^{2}+b ^{2}-2ab \cos \gamma$$

directrix · Answer

That is what we will use.

directrix · Answer

The square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.

anonymous · Answer

so our equation will be $$400^{2}=100^{2}+x ^{2}-2(100)(x)(\cos45)$$ right?

directrix · Answer

Yes.

anonymous · Answer

Okay. So |dw:1361768675207:dw|