A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth
To find the distance between the two points (3, 2) and (7, 8), we can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case:
x1 = 3
y1 = 2
x2 = 7
y2 = 8
Plugging these values into the distance formula, we get:
d = √((7 - 3)^2 + (8 - 2)^2)
d = √(4^2 + 6^2)
d = √(16 + 36)
d = √52
d ≈ 7.21
Therefore, the distance between the two points is approximately 7.21 units. Rounding to the nearest hundredth, the answer is 7.21 units.
The shortstop needs to make the throw from the base path between second and third base to first base, which is located on the same side of the field. Since the field is square, the distance from second base to first base is the same as the distance from third base to home plate.
Let's call the distance from second base to first base "x". We know that the distance from second base to home plate is 90 feet (since the distance from each base to home plate is 90 feet in baseball).
Using the Pythagorean theorem, we can set up the following equation:
x^2 = 90^2 - 30^2
x^2 = 8100 - 900
x^2 = 7200
Taking the square root of both sides, we get:
x = √7200
x ≈ 84.9
Therefore, the shortstop needs to throw the ball approximately 84.9 feet to first base. Rounding to the nearest tenth, the answer is 84.9 feet.
Apply the Pythagorean theorem to find the two points round your answer to the nearest hundredth the two points are (3,2) and (7,8)
fins the slant of the height of the square pyramid the width is 16 and the Hight is 15
To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height, represented by "l," can be found by equating the square of the slant height to the sum of the square of the height and half the square of the width.
Using the given values:
Height (h) = 15
Width (w) = 16
We can calculate the slant height as follows:
l^2 = h^2 + (w/2)^2
l^2 = 15^2 + (16/2)^2
l^2 = 225 + 8^2
l^2 = 225 + 64
l^2 = 289
Taking the square root of both sides, we find:
l = √289
l = 17
Therefore, the slant height of the square pyramid is equal to 17 units.
find the length of the diagonal of the prism the Hight of it is 12 cm the width of it is 3 cm and the length of it is 4 cm
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. The diagonal length, represented by "d," can be found by equating the square of the diagonal length to the sum of the squares of the length, width, and height.
Using the given values:
Height (h) = 12 cm
Width (w) = 3 cm
Length (l) = 4 cm
We can calculate the diagonal length as follows:
d^2 = l^2 + w^2 + h^2
d^2 = (4 cm)^2 + (3 cm)^2 + (12 cm)^2
d^2 = 16 cm^2 + 9 cm^2 + 144 cm^2
d^2 = 169 cm^2
Taking the square root of both sides, we find:
d = √169
d = 13 cm
Therefore, the length of the diagonal of the rectangular prism is equal to 13 cm.
the great pyramid of Giza in egypt has a square base with edge length of 230.5 m and a slant height of 180.2 find the height of the pyramid round your answer to the nearest tenth
To find the height of the pyramid, we can use the Pythagorean theorem. The slant height (l) and the height (h) of the pyramid, along with half the length of the base (b/2), form a right triangle.
Using the given values:
Base length (b) = 230.5 m
Slant height (l) = 180.2 m
We can calculate the height as follows:
h^2 = l^2 - (b/2)^2
h^2 = (180.2 m)^2 - (230.5 m / 2)^2
h^2 = 32544.04 m^2 - 26560.25 m^2
h^2 = 5983.79 m^2
Taking the square root of both sides, we find:
h = √5983.79 m
h ≈ 77.3 m
Therefore, the height of the pyramid is approximately 77.3 meters. Rounded to the nearest tenth, the answer is 77.3 meters.
To find the distance the shortstop needs to throw the ball, we can use the Pythagorean theorem since we have a right triangle. The distance from second base to first base represents the hypotenuse of the triangle, and the distance from the shortstop to second base represents one of the legs.
Let's label the distances:
- Distance from second base to first base (hypotenuse): c (unknown)
- Distance from shortstop to second base (leg): a (30 feet)
- Distance from shortstop to first base (leg): b (unknown)
Using the Pythagorean theorem, we have the formula:
a^2 + b^2 = c^2
Substituting the known values into the formula, we get:
30^2 + b^2 = c^2
Now we can solve for c by finding the square root of both sides:
b^2 = c^2 - 30^2
b = √(c^2 - 900)
To simplify this equation, we can approximate the square root of (c^2 - 900) as c itself, assuming the distance is significantly greater than 30 feet.
Therefore, the approximate distance the shortstop needs to throw the ball to first base is 30 feet.