Ace the North Carolina RADAR State Exam 2025 – Speed Your Way to 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

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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:

\[ W = 2 \times D \times 0.0962 \]

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