Question

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? 57° 50° 40° 33°

Answer 1

The answer is 40degree using soacahtoa

Answer 2

B.
`50^(\circ)`.

Explanation:

Let the sun be x degrees above the horizon.

We have been given that a skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long.

We can see from our attachment that skyscraper and shadow forms a right triangle with respect to ground.

We know that tangent relates the opposite side of right triangle to its adjacent, so we can set an equation as:

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

`\text{tan}(x)=(396)/(332)`

Using arctan we will get:

`x=\text{tan}^(-1)((396)/(332))`

`x=50.02407525854^(\circ)\approx 50^(\circ)`

Therefore, the sun is 50 degrees above the horizon at that time.