A soccer field is a rectangle 90 meters wide and 120 meters long. The soccer team ran from one corner to the other corner, along the diagonal of the soccer field.
How far, in meters, did the players run?
To find the distance the players ran, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.
In this case, the width of the soccer field is the length of one leg of the triangle (90 meters), the length of the field is the other leg of the triangle (120 meters), and the distance the players ran is the hypotenuse.
Using the Pythagorean theorem, we have:
Distance^2 = Width^2 + Length^2
Distance^2 = 90^2 + 120^2
Distance^2 = 8100 + 14400
Distance^2 = 22500
Taking the square root of both sides, we get:
Distance = √22500
Distance ≈ 150.49 meters
Therefore, the players ran approximately 150.49 meters.
If m∠W = 105° and m∠Y = 75°, then m∠X =
Responses
A 10°.10°.
B 20°.20°.
C 30°.30°.
D 75°.75°.
E 120°.
To find m∠X, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find m∠X by subtracting the measures of angles ∠W and ∠Y from 180 degrees.
m∠X = 180° - m∠W - m∠Y
m∠X = 180° - 105° - 75°
m∠X = 180° - 180°
m∠X = 0°
So, the measure of angle X is 0 degrees.
None of the given answer choices match 0°, which suggests there may be a mistake or typo in the options provided. Therefore, it is not possible to determine the correct answer based on the given options.
Joseph completely covered the floor of his square office with carpet. He used 148 ft2 of carpet. Which measurement is closest to the length of one side of Joseph’s office in feet?
Responses
A 11 ft11 ft
B 27 ft27 ft
C 12 ft12 ft
D 74 ft
To find the length of one side of Joseph's office, we need to find the square root of the area of the office.
Since Joseph used 148 ft2 of carpet to completely cover the floor, the area of the office is 148 ft2.
Taking the square root of 148 ft2, we have:
sqrt(148) ≈ 12.17 ft
The measurement closest to the length of one side of Joseph's office in feet is 12 ft.
Among the given answer choices, the closest measurement to 12 ft is option C: 12 ft.
Question:
If m∠W = 105° and m∠Y = 75°, then m∠X =
Responses:
* 10°.
* 20°.
* 30°.
* 75°.
* 120°.
There's a triangle that has a line on top on the line there's Point W and on the top of the triangle there's Point Z and on the right side there's Point Y and on the left side and Point X
To find the distance that the players ran along the diagonal of the soccer field, we can use the Pythagorean theorem. The theorem 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 other two sides.
In this case, the width and length of the soccer field form the two sides of the right-angled triangle, and the diagonal represents the hypotenuse. So, we can use the formula to calculate the distance.
Let's denote the width of the field as W = 90 meters and the length as L = 120 meters.
Using the Pythagorean theorem, we have:
Diagonal^2 = Width^2 + Length^2
Diagonal^2 = 90^2 + 120^2
Diagonal^2 = 8100 + 14400
Diagonal^2 = 22500
Now, we can take the square root of both sides to find the diagonal:
Diagonal = √22500
Diagonal ≈ 150.05 meters (rounded to two decimal places)
So, the players ran approximately 150.05 meters along the diagonal of the soccer field.