QuestionHow far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: $d = \sqrt{(60^2 + 60^2)}$ .

Studdy Solution

STEP 1

Assumptions1. The softball field is in the shape of a square (diamond). . The distance between each base is60 feet.
3. The catcher is at home plate and wants to throw to second base.
4. We are looking for the distance from home plate to second base, which is the diagonal of the square.

STEP 2

In a square, the diagonal can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. $Diagonal = \sqrt{Side^2 + Side^2}$

STEP 3

Now, plug in the given value for the side length to calculate the diagonal.
$Diagonal = \sqrt{60^2 +60^2}$

STEP 4

implify the equation.
$Diagonal = \sqrt{3600 +3600}$

STEP 5

Calculate the sum under the square root.
$Diagonal = \sqrt{7200}$

STEP 6

Calculate the square root to find the diagonal length.
$Diagonal = \sqrt{7200} =84.85\, feet$ The catcher must throw approximately84.85 feet from home plate to second base.

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QuestionHow far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: $d = \sqrt{(60^2 + 60^2)}$ .

Studdy Solution

STEP 1

Assumptions1. The softball field is in the shape of a square (diamond). . The distance between each base is60 feet.
3. The catcher is at home plate and wants to throw to second base.
4. We are looking for the distance from home plate to second base, which is the diagonal of the square.

STEP 2

STEP 3

Now, plug in the given value for the side length to calculate the diagonal.
$Diagonal = \sqrt{60^2 +60^2}$

STEP 4

implify the equation.
$Diagonal = \sqrt{3600 +3600}$

STEP 5

Calculate the sum under the square root.
$Diagonal = \sqrt{7200}$

STEP 6

Calculate the square root to find the diagonal length.
$Diagonal = \sqrt{7200} =84.85\, feet$ The catcher must throw approximately84.85 feet from home plate to second base.

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QuestionHow far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: d=(602+602)d = \sqrt{(60^2 + 60^2)}d=(602+602)​.

Studdy Solution

STEP 1

Assumptions1. The softball field is in the shape of a square (diamond). . The distance between each base is60 feet.3. The catcher is at home plate and wants to throw to second base.4. We are looking for the distance from home plate to second base, which is the diagonal of the square.

STEP 2

STEP 3

Now, plug in the given value for the side length to calculate the diagonal.Diagonal=602+602Diagonal = \sqrt{60^2 +60^2}Diagonal=602+602​

STEP 4

implify the equation.Diagonal=3600+3600Diagonal = \sqrt{3600 +3600}Diagonal=3600+3600​

STEP 5

Calculate the sum under the square root.Diagonal=7200Diagonal = \sqrt{7200}Diagonal=7200​

STEP 6

Calculate the square root to find the diagonal length.Diagonal=7200=84.85 feetDiagonal = \sqrt{7200} =84.85\, feetDiagonal=7200​=84.85feetThe catcher must throw approximately84.85 feet from home plate to second base.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: $d = \sqrt{(60^2 + 60^2)}$ .

Assumptions1. The softball field is in the shape of a square (diamond). . The distance between each base is60 feet.
3. The catcher is at home plate and wants to throw to second base.
4. We are looking for the distance from home plate to second base, which is the diagonal of the square.

Now, plug in the given value for the side length to calculate the diagonal.
$Diagonal = \sqrt{60^2 +60^2}$

implify the equation.
$Diagonal = \sqrt{3600 +3600}$

Calculate the sum under the square root.
$Diagonal = \sqrt{7200}$

Calculate the square root to find the diagonal length.
$Diagonal = \sqrt{7200} =84.85\, feet$ The catcher must throw approximately84.85 feet from home plate to second base.