Question

The angle of depression of the light to the nearest minute is

Answer 1

θ = 37° 30'

Step-by-step explanation:

The angle of depression has the same measure as the angle of elevation, so a trigonometric function that related the sides of the triangle and the angle of elevation θ is tangent. Then:

`\text{tan }\theta\text{ =}(39.57)/(51.56)`

Therefore, the value of θ is:

`\begin{gathered} \tan \text{ }\theta\text{ = 0.7674} \\ \theta=\tan ^(-1)(0.7674) \\ \theta=37.50 \end{gathered}`

So, in grades and minutes, we get:

θ = 37.50 = 37° 30'

Therefore, the angle of depression is 37° 30'