What is the answer when theta is 70

Question

A patrol car is parked 55 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 22 revolutions per minute. How fast is the light beam moving (in ft/sec) along the wall when the beam makes angles of 𝜃 = 30°, 𝜃 = 60°, and 𝜃 = 70° with the line perpendicular from the light to the wall? (Round your answers to two decimal places.)

Answer 1

Let x be the light beam position on the wall to the a line, perpendicular to the wall, from the light

dθ/dt = 22 rev/min = 22 (2π)/60 = 22 π/30 rads/sec Assume the light is rotating counter clockwise.

tan(θ) = x/55

Take the derivative of both side of the equal sign empirically.

sec² (θ) dθ/dt = (1/55) dx/dt.

Need to find dx/dt when θ = 30°, 60° and 70°.

dx/dt = 55sec²(θ)dθ/dt ft/sec

sec(30°) = 2/√3

sec(60°) = 2

sec(70°) ≈ 3.92

Can you substitute in the values to find dx/dt at the 3 request angles?