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In a circle with radius r, a central angle theta intercepts a chord of length c,

ID: 2878530 • Letter: I

Question

In a circle with radius r, a central angle theta intercepts a chord of length c, where theta = cos^- 1 (1 - c^2/2 r^2). An airplane at 2115 feet flies directly over a gun that has a range of 2397 feet, as shown in the figure. What is the measure in degrees of the angle for which the airplane is within range of the gun? The angle for which the airplane is within range of the gun is (Round the final answer to the nearest tenth as needed. Round all intermediate values to four decimal places as needed.)

Explanation / Answer

at the maximum range, cos t = 2115 / 2397
t = cos^-1 (2115 / 2397) = 28.072 degrees
from vertical, the gun has a range of 28.072 degrees