A searchlight is trained on the side of a tall building. As the light rotates, t

Question

A searchlight is trained on the side of a tall building. As the light rotates, the spot it illuminates moves up and down the side of the building. That is, the distance D between ground level and the illuminated spot on the side of the building is a function of the angle ? formed by the light beam and the horizontal (see the accompanying figure). If the searchlight is located a=99 m from the building, find the rate at which D is changing with respect to ? when ?=45? . Express your answer in units of meters/degree.

Chapter 2, Section 2.5, Question 033 Incorrect. A searchlight is trained on the side of a tall building. As the light rotates, the spot It Illuminates moves up and down the side of the building. That is, the distance D between ground level and the illuminated spot on the side of the building is a function of the angle formed by the light beam and the horizontal (see the accompanying figure. If the searchlight is located = 99 m from the building, find the rate at which D is changing with respect to when 6-45. Express your answer in units of meters/degree. Round your answer to two decimal places dD 198 meters/degree the tolerance is +/-290

Explanation / Answer

D = a tan()
dD/d = 99 sec²()

At = 45°,
dD/d = 99 sec²(45°)
= 99(2)²
= 198 meters/degree

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