Question

A balloon rises at the rate of 8 feet per second from a point on the ground 12 feet from an observer. To 2 decimal places in radians per second, find the rate of change of the angle of elevation when the balloon is 9 feet above the ground. Type your answer in the space below. If your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).

Answer 1

Step-by-step explanation:

To solve this related rates (of change) problem:

Let y = the height of the balloon and let θ = the angle of elevation.

We are told that dy/dt=8 ft/sec.

We are asked to find dθ/dt when y=25 ft.

Draw a right triangle with base = 60 ft (that doesn't change),

height y and angle opposite height θ.

Then

 tanθ=y60

 and y=60tanθ.

Differentiating with respect to t gives us:

ddt(y)=ddt(60tanθ).

dydt=60sec2θdθdt.

We are asked to find dθ/dt when y=25.

We have: 8=60sec2θdθdt, so

dθdt=860cos2θ=215cos2θ.

We need cosθ when y=25.

With base = 60 and height = 25, we get hypotneuse c=√60

.

now please mark me as brainliest.❤