A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door?

Question

Stacy Sharp

Mathematics

29 November, 11:59

A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door?

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Answers (1)

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Myla Mcdowell · Answer 1

Here we have a 90 degrees triangle where we can use trigonometric functions.

Here we can use tan (x) function because it requires legs of triangle that are given and inverse function of tan (x) will than give us asked angle

tan (x) = 7.4/9.3 = 0.7956

x = arctan (0.7956) = 38.505 ≈ 39 degrees.