We want to know if the referee can hear the player's question. Let's start by looking at the diagram!
We can see that the referee's ear is 12 feet above the ground and that the player's mouth is 5 feet above the ground. Let's calculate the height difference between the referee's ear and the player's mouth.
12-5= 7
The referee's ear is 7 feet above the player's mouth. Now, we can draw a triangle with two sides measuring 7 feet and 24 feet. The missing side will be the distance between the referee's ear and the player's mouth. Let's do it!
Notice that the distance between the referee's ear and the player's mouth is the hypotenuse of a right triangle. Therefore, we can use the Pythagorean Theorem to find the length of the missing side.
a^2+b^2=c^2
In this formula, a and b are the legs and c is the hypotenuse of a right triangle. Let's identify a, b, and c on the diagram.
We can see that a= 24 feet and b= 7 feet. Let's substitute these values into the formula.
The distance from the player's mouth to the referee's ear is 25 feet. We know that the player's voice travels 30 feet and that 25 is less than 30. This means that the referee can hear the player's question because he is within hearing range.
