Question

tan θ = y/360
sec²θ dθ/dt = 1/360 dy/dt
because sec θ = 1/cos θ, this equation can be rewritten as shown.
sec²θ dθ/dt = 1/360 dy/dt
dθ/dt = cos²θ/360 dy/dt
to find the value of cos θ, first use the pythagorean theorem to find the length of the hypotenuse when y = 480 ft
√(360² + 480²) = □ ft
print
clear all

Explanation:

Step1: Apply Pythagorean Theorem

\[

$$\begin{align*} &\text{The Pythagorean Theorem for a right - triangle is }c=\sqrt{a^{2}+b^{2}}\\ &\text{Here }a = 360\text{ and }b = 480\\ &\text{So, }c=\sqrt{360^{2}+480^{2}} \end{align*}$$

\]

Step2: Calculate the value

\[

$$\begin{align*} \sqrt{360^{2}+480^{2}}&=\sqrt{129600 + 230400}\\ &=\sqrt{360000}\\ &=600 \end{align*}$$

\]

Answer:

600