A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction cap n 20 degrees cap e Which diagram represents the boat’s current distance, x , from the pier?
Answer
A
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by vector 15 miles and the x-axis is 20 degrees.
B
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by a vertical line and vector 15 miles is 20 degrees.
C
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with a vertical line and vector 15 miles is 20 degrees.
D
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with the x-axis and vector 15 miles is 20 degrees.
Explanation
“N 20° E” means travel 20° east of north, so the second 15-mile vector points up and to the right, with its angle measured from a vertical line. The first 15-mile leg points due east along the x-axis, and the boat’s distance from the pier is the vector from the origin to the endpoint. These features match choice C.
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