Question

4 Select the correct answer. A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long. At what angle is the sun above the horizon at that time? OA. 57° B. 50° Oc. 40° OD. 33°

Answer 1

Notice that the ray of sun the skyscraper and the shadow makes a right triangle thus the angle that we are looking for can be defined by the trigonometric function:

`\tan \theta=\frac{\text{opposite side}}{\text{adjacent side}}`

referring to the angle that is marked in blue, the opposite side is 396m and the adjacent side is 332 m. Thus,

`\tan \theta=\frac{\text{opposite side}}{\text{adjacent side}}=(396)/(332)`

In order to get the value of the angle, we need to get the inverse tangent .

`\begin{gathered} \tan \theta=(396)/(332) \\ \theta=\tan ^(-1)((396)/(332)) \\ \theta=50.02^(\circ) \end{gathered}`

Answer:

`B)\theta=50.02^(\circ)`