Calculus Related Rate - Kite problem -- Juda math

Related Rate - kite moving horizontally calculating the rate of change in the angle.

Stewart 3.9 #24

[johnnolen]

Nice solution but you did a bunch of trig that was completely unnecessary. To begin with you have tan θ = 100/x. This gives you sec^2 θ · dθ/dx = - 100/x^2. There's no reason to use the quotient rule. Use the reciprocal rule instead. Substituting the ratio that defines secant on the left hand side, 200^2/x^2·dθ/dx = -100/x^2. The factors of x^2 cancel on both sides and you're left with dθ/dx = - 100/200^2 = - 1/400. Now dθ/dt = dθ/dx · dx/dt. Thus dθ/dt = (-1/400 rad/ft)(8 ft/s) = -1/50 rad/s. No need to figure out θ or solve for x or any of that stuff. Just because it's trig doesn't mean it has to be hard. 😃