An explorer is caught in a whiteout (in which the snowfall is so thick that the

Question

An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.4 km, but when the snow clears, he discovers that he actually traveled 8.9 km at 53 degeree north of due east. How far (in km) must he now travel to reach base camp?

i did

let a = < 8.9 cos53, 8.9 sin 53>

b = <0.5.4>

then let vecto c = <x,y> be the required vector an explorer must travel,

a + c=b                                                                   

8.9 cos 53 + x = 0                                  8.9 sin53 + y=5.4

x= -8.17                                                    y= 1.88

total distance = x2+y2=8.38 km

I am trying to do this in wiley plus but the answer is incorrect. Can someone help me out with this?

Explanation / Answer

First you need to find the x and y components of his travel (which you did, but maybe not in the manner in which i would have done it.)

y (north) = 8.9 cos 53 = 5.356154 miles

and

x (east) = 8.9 cos 53 = 7.107856 miles

So just take the the 5.4 north he was supposed to travel north and subtract from that 5.356154 miles. That will be your y component of your triangle. (or A)

7.107856 east was completely in the wrong directions so set the entire value as the y component of your triangle. (or B)

A^2 + B^2 = C^2

Where C is you total distance he has to travel to return. Hopefully that gets you the right answer.

(P.S. sorry for not using a more vector oriented math, hopefully all you needed was the answer)

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