https://file.aiquickdraw.com/mathbot/file/172610530121117faoudv.jpg

To solve this problem, we need to compute the radar speed reading affected by the "cosine effect." The radar speed reading is given by the product of the actual speed of the vehicle and the cosine of the angle between the radar gun and the direction of the moving vehicle.

### Given:
- Actual speed of the vehicle = 89 mph
- Angle between the radar gun and the vehicle = 15 degrees

### Formula:
The radar speed reading \( R \) can be calculated using the formula:
\[
R = \text{Actual speed} \times \cos(\theta)
\]
where:
- \(\text{Actual speed} = 89 \) mph
- \(\theta = 15^\circ\)

### Calculation:
Now, let's compute the value:

\[
R = 89 \times \cos(15^\circ)
\]

Using a calculator, we find:
\[
\cos(15^\circ) \approx 0.9659
\]

Therefore:
\[
R = 89 \times 0.9659 \approx 85.96 \, \text{mph}
\]

To the nearest hundredth, the radar speed reading is **85.97 mph**.

### Conclusion:
The correct answer is **C) 85.97 mph**.

Would you like further details or have any additional questions? Here are some related questions you might be interested in:

1. How does the cosine effect influence radar speed readings at different angles?
2. What happens to the radar reading as the angle between the vehicle and the radar gun increases?
3. How is the cosine function used in other real-life applications, such as physics or engineering?
4. Why is the cosine effect important for law enforcement using radar guns?
5. What are other mathematical effects that impact measurements in real-world scenarios?

**Tip:** Remember that the cosine of an angle decreases as the angle increases from 0 to 90 degrees, which means the radar reading will be lower as the angle widens.

Any offset between a stationary radar gun and a moving target creates a 'cosine effect' that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the radar speed reading is the product of the actual reading and the cosine of the angle. Find the radar reading to the nearest hundredth for the auto shown in the figure, with a 15-degree angle and actual speed of 89 mph.

Learn how to calculate radar speed using the cosine effect, applied to an actual vehicle speed of 89 mph and a 15-degree angle offset. The step-by-step solution demonstrates the use of the cosine function in trigonometry, ideal for students in Grades 10-12.

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