To find out how far the car travels east when it's traveling 45 km at an angle of 35° north of east, you can use trigonometry.
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Draw a Right Triangle: Picture the situation in a coordinate system where the horizontal axis (x-axis) represents east and the vertical axis (y-axis) represents north. The hypotenuse of the triangle represents the distance the car travels (45 km), and the angle between the hypotenuse and the east direction is 35°.
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Use the Cosine Function: The adjacent side of the triangle (the distance traveled east) can be found using the cosine function, which is defined as the ratio of the adjacent side to the hypotenuse. In this case: \[ \text{East distance} = \text{Hypotenuse} \times \cos(\text{angle}) \]
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Substitute the Values: \[ \text{East distance} = 45 , \text{km} \times \cos(35°) \]
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Calculate the Cosine: Use a calculator to find \(\cos(35°)\). It is approximately \(0.8192\).
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Calculate the Distance: \[ \text{East distance} = 45 , \text{km} \times 0.8192 \approx 36.864 , \text{km} \]
So, the car travels approximately 36.86 km east.
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