There are four different angles of rotation that fits the description in the exercise. The central pole runs along the y-axis.
58^(∘)
122^(∘)
238^(∘)
302^(∘)
Practice makes perfect
To answer this exercise, we should illustrate the position(s) where Shinna could be when she is 53 horizontal feet from the central pole which runs along the y-axis.
As we can see, Shinna can be at four places on The Screamer when she is 53 horizontal feet from the central pole, which results in four angles of rotation.
To calculate these possible angles of rotation, we should start with determining the angle in the first quadrant. To do that, we recognize that this angle is a non-right angle in a right triangle with an hypotenuse equal to the radius of The Screamer, 100 feet, and an adjacent leg of 53 feet.
With this information, we can calculate the first angle of rotation using the cosine ratio.
The first angle of rotation is 58 ^(∘). To calculate the three remaining angles, we have to recognize the following relationships between the angle in the first quadrant, our reference angle, and the three other angles.
Since we know that θ= 58^(∘), we can find the remaining three angles of rotation.
180^(∘)- 58^(∘)&=122^(∘)
180^(∘)+ 58^(∘)&=238^(∘)
360^(∘)- 58^(∘)&=302^(∘)
