Question

A railroad track has an angle of elevation of 1.00°. what is the difference in height (in ft) of two points on the track 2.00 mi apart? (1 mi = 5,280 ft. round your answer to three significant digits.)

Answer 1

To find the difference in height of two points on the railroad track, we can use trigonometry. With an angle of elevation of 1.00° and a distance of 2.00 miles, we can calculate the height difference to be approximately 185 ft.

Step-by-step explanation:

To find the difference in height between two points on the railroad track, we can use the concept of trigonometry. The angle of elevation of 1.00° represents the angle between the horizontal ground and the track. We can use this angle and the distance of 2.00 miles to calculate the height difference.

First, we convert the distance to feet by multiplying it by 5,280 (1 mi = 5,280 ft). So, 2.00 mi * 5,280 ft / mi = 10,560 ft.

Next, we can use the trigonometric function tangent to calculate the height difference. tan(angle) = height difference / distance. Substituting the values, tan(1.00°) = height difference / 10,560. Rearranging the equation, height difference = 10,560 * tan(1.00°).

Calculating this using a calculator, the height difference is approximately 184.933 ft. Rounded to three significant digits, the difference in height is 185 ft.