Answer:
Every 5 seconds the beam rotates 90 degrees;
![90^(\circ)](https://img.qammunity.org/2023/formulas/mathematics/college/jkua6oe5rfk01cigmto0hary2opy7kzhco.png)
Step-by-step explanation:
Given that the beam of a lighthouse makes one complete revolution every 20 seconds.
one complete revolution is;
![360^{\circ^{}}](https://img.qammunity.org/2023/formulas/mathematics/college/v4o2gxbfo9w5e88pd40d5dr6xr2v8gmg9k.png)
The rate of rotation is;
![r=(360^(\circ))/(20)=18^(\circ)\text{ per second}](https://img.qammunity.org/2023/formulas/mathematics/college/4vz5o9x385ezprlmj0xz2f7iqbzsurlr76.png)
The number of degrees it will rotate in 5 seconds is;
![\begin{gathered} x=5* r=5*18^(\circ)per\text{ second} \\ x=90^(\circ) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/i802y9f81ye8ui02oy6vzer18br8aou7gq.png)
Therefore, every 5 seconds the beam rotates 90 degrees;
![90^(\circ)](https://img.qammunity.org/2023/formulas/mathematics/college/jkua6oe5rfk01cigmto0hary2opy7kzhco.png)