North Carolina RADAR State Practice Exam

At what distance down the road is a beam with an 11-degree angle more than 38 feet wide?

1. 100 feet

2. 200 feet

3. 300 feet

4. 400 feet

The correct answer is: 200 feet

To determine at what distance down the road a beam with an 11-degree angle is more than 38 feet wide, it’s essential to use basic trigonometry. The width of the beam can be conceptualized as the horizontal distance across the beam from one edge to the other, depending on the distance from the source of the beam. The formula to calculate the width of the beam at a given distance (d) from the source, given an angle (θ), is: Width = d × tan(θ). Thus, when we set the width equal to 38 feet, we can express the equation as follows: 38 feet = d × tan(11 degrees). To find d, we rearrange the equation: d = 38 feet / tan(11 degrees). By calculating the value of tan(11 degrees) and plugging it into the equation, we can determine the distance at which the beam reaches more than 38 feet in width. Calculating this gives: tan(11 degrees) ≈ 0.1944 (approximately), So, d ≈ 38 feet / 0.1944 ≈ 195.5 feet. Rounding this value, we conclude that at a distance of about 200 feet