Answer to Question #248143 in Calculus for kae

Question #248143

Consider the given right triangle with legs of length x cm. and y cm. and angle θ radians. If x is decreasing at the rate of 3 cm/min. and y is increasing at the rate of 4 cm/min., at what rate is angle θ changing when x=5 cm. and y=2 cm. ?


1
Expert's answer
2021-10-08T09:39:20-0400

"y=xtan\\theta"

"\\theta=tan^{-1}(y\/x)"

"\\frac{d\\theta}{dt}=\\frac{1}{1+(y\/x)^2}\\cdot \\frac{y'x-x'y}{x^2}=\\frac{1}{1+(2\/5)^2}\\cdot \\frac{4\\cdot 5-3\\cdot 2}{5^2}=\\frac{14}{29}"


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