of the curve is vien signllly CiCTunt figure. This inclination is the superelevation. For safety reasons, it iS im. the curve's radius and superelevation be correct for a given speed limit. If an automobile is traveling at velocity V (in feet per second), the safe radius R, in feet, for a curve with superelevation 0 is modeled by the formula V2 %3D 8(f + tan 0)' where f and g are constants. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.) 77. A roadway is being designed for automobiles traveling at 45 mph. If 0 = 3°, g = 32.2, and f = 0.14, calculate R to the nearest foot. (Hint: 45 mph = 66 ft per sec) 78. Determine the radius of the curve, to the nearest foot, if the speed in Exercise 77 is increased to 70 mph. 79. How would increasing angle 0 affect the results? Verify your answer by repeating Exercises 77 and 78 with 0 = 4°.

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A: Explanation of the answer is as follows

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.