Answer:
To calculate the size of the serving angle A in the diagram of the volleyball court, you can use trigonometry.
You have the following information:
The distance from point A to point C is 9 meters.
The distance from point A to point B is 31 meters.
To find angle A, you can use the inverse tangent (arctan) function:
�
=
arctan
(
�
�
�
�
)
A=arctan(
AC
BC
)
Substitute the values:
�
=
arctan
(
31
9
)
A=arctan(
9
31
)
Now, calculate the angle:
�
≈
arctan
(
3.444
)
≈
73.4
8
∘
A≈arctan(3.444)≈73.48
∘
Rounded to the nearest degree, the size of the serving angle A is approximately 73 degrees.
Explanation:
Sure, I'll explain it in a simpler way:
Imagine you're standing at point A on the volleyball court, and you want to serve the ball towards point C or point B. Point C is 9 meters away, and point B is 31 meters away from you.
To find out how wide the angle is between where you stand (point A) and where you want to serve the ball (between points C and B), we can use a special math trick. It's like saying, "How much do I need to aim to the left or right?"
We use something called "arctan" to figure it out. When we do the math, we find that the angle A is about 73 degrees. So, you need to aim your serve at about a 73-degree angle to get the ball between points C and B on the other side of the court.