Salma went on a walk in her neighborhood.
First, she walked on a straight road for
\[2\text{ km}\]. The direction of the road is a
\[20\degree\] rotation from east.
Then, she turned into a different road whose direction is a
\[100\degree\] rotation from east. She walked on that road for
\[3\text{ km}\].
How far is Salma from her starting point at the end of the walk?
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Salma went on a walk in her neighborhood. She first walked 2 kilometers on a road that is 20 degrees from east, then turned to another road that is 100 degrees from east and walked 3 kilometers. We need to find how far she is from her starting point. Let's set up a coordinate system with east as the positive x-axis and north as the positive y-axis.
Now let's break down each walking segment into x and y components using trigonometry. For the first segment of 2 kilometers at 20 degrees from east: x1 equals 2 cosine 20 degrees, which is 1.88 kilometers, and y1 equals 2 sine 20 degrees, which is 0.68 kilometers. For the second segment of 3 kilometers at 100 degrees from east: x2 equals 3 cosine 100 degrees, which is negative 0.52 kilometers, and y2 equals 3 sine 100 degrees, which is 2.95 kilometers.