North Carolina RADAR State Practice Exam

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Prepare for the North Carolina RADAR State Exam with essential insights and practice questions to boost your confidence. This comprehensive resource will guide you through the exam requirements, helping you maximize your chances of success.

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At what distance down the road is a beam with an 11-degree angle more than 57 feet wide?

200 feet
250 feet
300 feet
350 feet

The correct answer is: 300 feet

To determine the distance down the road at which a beam with an 11-degree angle is more than 57 feet wide, we can utilize some basic trigonometry, specifically the tangent function, which relates angles to opposite and adjacent sides in a right triangle. The width of the beam at a given distance can be calculated using the formula for the width (W) of the beam at that distance (D) given an angle (θ): \[ W = 2 \times D \times \tan\left(\frac{θ}{2}\right) \] Here, θ is the angle of the beam (11 degrees), and we want W to be greater than 57 feet. First, we need to find out what distance D makes W greater than 57 feet: 1. Calculate $\tan\left(\frac{11}{2}\right)$: $\frac{11}{2} = 5.5$ degrees. The tangent of 5.5 degrees can be calculated (or found using a calculator) to be approximately 0.0962. 2. Plugging that value into the formula gives us: \[ W = 2 \times D \times 0.0962 \]