The discussion focuses on calculating the rate of change of the angle θ (d(θ)/dt) as a plane approaches an observer from an altitude of 5 miles, with a horizontal distance change rate (dx/dt) of -600 mi/h. The correct approach involves using the relationship tan(θ) = height/distance, where the height remains constant at 5 miles. The formula derived for d(θ)/dt is based on the derivative of arctan(500/x), leading to the conclusion that the observer must consider the negative rate of change in distance as the plane approaches.
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kingdomof said:Homework Statement
A plane is approaching an observer from an altitude of 5 mi at a dx/dt of 600 mi/h. Find the d(theta)/dt when theta is 30 degrees, 60 degrees, and 75 degrees.
Homework Equations
tan(theta) = x/y
5csc(theta) = r
The Attempt at a Solution
For my d(theta)/dt I had the formula of 3000/(5csc(theta))^2
The answers I had were wrong according to the text.
Please help.