The distance from home plate to dead center field in a certain baseball stadium is 409 feet. A baseball diamond is square with a distance from home plate to first plate base 90 feet. How far is it from first base to dead center field?
I also need help setting this up.
Since the diamond's diagonal is along the direction of travel, the angle between the direction and the baseline is 135°.
The distance from 2nf base to dcf = 409-90√2
Now use the law of cosines to find the unknown distance:
d^2 = (409-90√2)^2 + 90^2 - 2(409-90√2)(90)cos 135°
d = 351.18 ft
Thank you!
To find the distance from first base to dead center field, we can use the Pythagorean theorem.
Step 1: Draw a diagram of the baseball diamond and the dead center field.
Step 2: Label the distance from home plate to first base as 90 feet.
Step 3: Label the distance from home plate to dead center field as 409 feet.
Step 4: Draw a right-angled triangle with one side representing the distance from first base to home plate (90 feet), another side representing the distance from home plate to dead center field (409 feet), and the hypotenuse representing the distance from first base to dead center field (which we want to find).
Step 5: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a is 90 feet and b is 409 feet.
Step 6: Use the formula c^2 = a^2 + b^2 to find the square of the hypotenuse.
Step 7: Substitute the known values into the formula: (distance from first base to dead center field)^2 = (90 feet)^2 + (409 feet)^2.
Step 8: Calculate the squares and add them: (distance from first base to dead center field)^2 = 8100 feet^2 + 167281 feet^2.
Step 9: Simplify the equation: (distance from first base to dead center field)^2 = 175381 feet^2.
Step 10: Take the square root of both sides to find the distance from first base to dead center field.
Therefore, the distance from first base to dead center field is approximately sqrt(175381) feet.
To find the distance from first base to dead center field, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right 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 other two sides.
In this case, the distance from home plate to first base is given as 90 feet, and the distance from home plate to dead center field is 409 feet. We want to find the distance from first base to dead center field, which will be the hypotenuse of a right triangle.
Let's label the distance from home plate to first base as "a", the distance from home plate to dead center field as "c", and the distance from first base to dead center field as "b".
Using the Pythagorean theorem, we have the equation:
a^2 + b^2 = c^2
Substituting the given values, we have:
90^2 + b^2 = 409^2
Simplifying the equation:
8100 + b^2 = 167281
Now, we can solve for "b" by subtracting 8100 from both sides of the equation:
b^2 = 167281 - 8100
b^2 = 159181
To find the square root of both sides to solve for "b":
b = sqrt(159181)
Using a calculator, we find:
b ≈ 398.973 feet
Therefore, the distance from first base to dead center field is approximately 398.973 feet.