North Carolina RADAR State Practice Exam

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

1. 200 feet

2. 250 feet

3. 300 feet

4. 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: \[ W = 2 \times D \times 0.0962 \]