2. April And May Play With Their Roller Skates At The Town Oval. From The Ce…

2. April and May play with their roller skates at the town oval. From the cente skates 4 meters east and then 5 meters south. May skates 5 meters wes -ight turn of 70° and skates 4 meters. Who is farther from the center of the oval?​

Answer:

To solve this problem, we need to find the distance of each skater from the center of the oval and compare them. Let’s assume that the center of the oval is point O.

April’s position can be represented as point A, which is 4 meters east and 5 meters south from point O. We can use the Pythagorean theorem to find the distance of A from O:

OA = √(4²+5²) = √(16+25) = √41 ≈ 6.4 meters

May’s position can be represented as point M, which is 5 meters west of point O. Then she turns 70° to the right and skates 4 meters. We can use trigonometry to find the distance of M from O. Let the angle between OM and the vertical be x:

sin(x) = 5/OM

OM = 5/sin(x)

After turning 70° to the right, the angle between OM and the vertical is 70°+90° = 160°. Therefore:

sin(160°) = 5/OM

OM = 5/sin(160°) ≈ 5.21 meters

Then May skated 4 meters further, so her final position is N, where NM = 4 meters. Using the Pythagorean theorem again, we can find the distance of N from O:

ON = √(OM²+NM²) ≈ 7.2 meters

Therefore, May is farther from the center of the oval than April.

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