To determine how far north the car travels, we can consider the situation as a right triangle where:
- The hypotenuse is 45 km (the distance traveled).
- The angle is 35° north of east.
We want to find the length of the side opposite to the angle, which corresponds to the distance traveled north. To do this, we use the sine function, which relates the opposite side to the hypotenuse.
The sine function is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In our case:
\[ \sin(35°) = \frac{\text{northward distance}}{45 \text{ km}} \]
Rearranging this, we can calculate the northward distance:
\[ \text{northward distance} = 45 \text{ km} \times \sin(35°) \]
Thus, the correct answer is:
A. Since we know the hypotenuse and want to calculate the opposite side of the given angle, we use the sine function multiplied by the hypotenuse.
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