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?
We can use the Pythagorean theorem to find the distance the players ran. The diagonal of the rectangle is the hypotenuse of a right triangle, with the sides being the width and length of the rectangle.
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 have:
distance = √22500
distance ≈ 150.9 meters
Therefore, the players ran approximately 150.9 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°.
The sum of the interior angles of a triangle is 180°. In triangle WXY, we have m∠W + m∠X + m∠Y = 180°.
Given that m∠W = 105° and m∠Y = 75°, we can substitute these values into the equation:
105° + m∠X + 75° = 180°.
Simplifying the equation, we have:
180° + m∠X = 180°.
Subtracting 180° from both sides, we have:
m∠X = 0°.
Therefore, m∠X is equal to 0°.
None of the answer choices listed matches 0°, so there's an error in the options provided.
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 ft74 ft
To find the length of one side of Joseph's square office, we need to find the square root of the area of the carpet used.
The area of the office is given as 148 ft^2.
Taking the square root of 148, we have:
sqrt(148) ≈ 12.17 ft.
Therefore, the measurement closest to the length of one side of Joseph's office in feet is 12 ft (Option C).
To find the distance the players ran from one corner to the other corner along the diagonal of the soccer 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 soccer field forms a right triangle, where the width of the field is one side and the length of the field is the other side. The diagonal of the field is the hypotenuse of the triangle.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
Diagonal^2 = Width^2 + Length^2
Diagonal^2 = 90^2 + 120^2
Diagonal^2 = 8100 + 14400
Diagonal^2 = 22500
Taking the square root of both sides to solve for the diagonal:
Diagonal = √22500
Diagonal ≈ 150.00 meters
Therefore, the players ran approximately 150.00 meters from one corner to the other corner along the diagonal of the soccer field.